Math Calculator

Triangle Calculator

Solve the triangle you know.

Triangle inputs

Choose the measurements you actually know.

Solve using

Each method retains its own source values; only active fields are validated.

Source, angle and output choices

Enter all three sides. A nondegenerate triangle must satisfy every strict triangle inequality.

Side

a

Use a finite decimal, scientific e notation or an integer fraction.

Side

b

Use a finite decimal, scientific e notation or an integer fraction.

Side

c

Use a finite decimal, scientific e notation or an integer fraction.

Output angle convention

Source length unit

The source unit interprets all known side, base and height values together.

Output length unit

Converts all solved sides, perimeter, altitudes, medians and circle radii.

Output area unit

Coverage converts independently, including international acres and hectares.

Rounded decimal places

Exact SSS radicals stay unchanged. Numerical trigonometry uses at most ten decimal places; very small nonzero values retain scientific views.

Load a worked example

Show triangle diagramShow all unit conversions

Sources support sixty significant decimal digits or sixty digits per fraction integer, one hundred eighty characters and scientific exponents from negative one hundred through positive one hundred. Exact squared magnitudes have an eighteen-hundred-digit limit. Trigonometry uses normalized numerical calculations with explicit side-ratio, angle and near-tangent limits. See the guide for these boundaries.

One triangle. Side and coverage quantities remain exact; angles and screen geometry are numerical.

Interpreted active measurements

a=3\,\mathrm{cm},\quad b=4\,\mathrm{cm},\quad c=5\,\mathrm{cm}

Triangle solution: triangle area

K=6\,\mathrm{cm}^{2}

Scalene, right

Rounded area view

K=6\,\mathrm{cm}^{2}

Perimeter

P=12\,\mathrm{cm}

Semiperimeter

s=6\,\mathrm{cm}

Solved triangle diagram

Vertices use equal horizontal and vertical scales. Side labels are opposite their matching capital-letter angles. Coordinates are numerical approximations; a reflected triangle represents the same measurements.

Calculation step by step

Interpret the active source
$a=3\,\mathrm{cm},\quad b=4\,\mathrm{cm},\quad c=5\,\mathrm{cm}$
Lowercase sides are opposite matching capital-letter angles. Only this method's active measurements are used.
Solve the selected triangle method
$s=\frac{a+b+c}{2},\quad K=\sqrt{s(s-a)(s-b)(s-c)}=6\,\mathrm{cm}^{2}$
The strict triangle inequality is checked exactly before Heron's formula. Rational source strings and verified radicals remain exact.
Read coverage and boundary separately
$P=a+b+c=12\,\mathrm{cm},\quad K=6\,\mathrm{cm}^{2}$
Perimeter is a length; coverage is an area. Output selectors convert them independently using exact physical unit definitions.
Derive altitudes, medians and circle radii
$h_a=\frac{2K}{a},\quad m_a=\frac{\sqrt{2b^2+2c^2-a^2}}{2},\quad r=\frac{K}{s},\quad R=\frac{abc}{4K}$
The same recovered triangle defines every additional quantity. In SSS mode, squared radical certificates preserve exact values; bounded simplification does not promise complete arbitrary factorization.

All triangle result details

Exact SSS values retain verified squared magnitudes. Trigonometric solutions and all angle views are numerical approximations. The rounded column never becomes a new source.

Triangle solution calculation details
Quantity	Exact or numerical value	Rounded view	Interpretation
Side $a$	$3\,\mathrm{cm}$	$3\,\mathrm{cm}$	Opposite the matching capital-letter angle.
Side $b$	$4\,\mathrm{cm}$	$4\,\mathrm{cm}$	Opposite the matching capital-letter angle.
Side $c$	$5\,\mathrm{cm}$	$5\,\mathrm{cm}$	Opposite the matching capital-letter angle.
Perimeter	$12\,\mathrm{cm}$	$12\,\mathrm{cm}$	Sum of all three boundary lengths.
Semiperimeter	$6\,\mathrm{cm}$	$6\,\mathrm{cm}$	Half the perimeter in output length units.
Triangle area	$6\,\mathrm{cm}^{2}$	$6\,\mathrm{cm}^{2}$	Coverage uses the independent output area unit.
Altitude to side $a$	$4\,\mathrm{cm}$	$4\,\mathrm{cm}$	Perpendicular distance to the line containing this side.
Median to side $a$	$\frac{1}{2}\sqrt{73}\,\mathrm{cm}$	$\approx\;4.272002\,\mathrm{cm}$	Connects the opposite vertex to the side midpoint.
Altitude to side $b$	$3\,\mathrm{cm}$	$3\,\mathrm{cm}$	Perpendicular distance to the line containing this side.
Median to side $b$	$\sqrt{13}\,\mathrm{cm}$	$\approx\;3.605551\,\mathrm{cm}$	Connects the opposite vertex to the side midpoint.
Altitude to side $c$	$\frac{12}{5}\,\mathrm{cm}$	$2.4\,\mathrm{cm}$	Perpendicular distance to the line containing this side.
Median to side $c$	$\frac{5}{2}\,\mathrm{cm}$	$2.5\,\mathrm{cm}$	Connects the opposite vertex to the side midpoint.
Incircle radius	$1\,\mathrm{cm}$	$1\,\mathrm{cm}$	Radius of the circle tangent to all three sides.
Circumcircle radius	$\frac{5}{2}\,\mathrm{cm}$	$2.5\,\mathrm{cm}$	Radius of the circle through all three vertices.
Angle $A$	$\approx\;36.869898^{\circ}$	$\approx\;36.869898^{\circ}$	Trigonometric angle view is numerical, including in exact SSS mode.
Angle $B$	$\approx\;53.130102^{\circ}$	$\approx\;53.130102^{\circ}$	Trigonometric angle view is numerical, including in exact SSS mode.
Angle $C$	$\approx\;90^{\circ}$	$\approx\;90^{\circ}$	Trigonometric angle view is numerical, including in exact SSS mode.

Perimeter in all length units

Triangle solution perimeter in all length units
Unit	Exact or numerical value	Rounded view
Nanometers	$12\times10^{7}\,\mathrm{nm}$	$120000000\,\mathrm{nm}$
Micrometers	$120000\,\mathrm{\mu m}$	$120000\,\mathrm{\mu m}$
Millimeters	$120\,\mathrm{mm}$	$120\,\mathrm{mm}$
Centimeters	$12\,\mathrm{cm}$	$12\,\mathrm{cm}$
Decimeters	$\frac{6}{5}\,\mathrm{dm}$	$1.2\,\mathrm{dm}$
Meters	$\frac{3}{25}\,\mathrm{m}$	$0.12\,\mathrm{m}$
Decameters	$\frac{3}{250}\,\mathrm{dam}$	$0.012\,\mathrm{dam}$
Hectometers	$\frac{3}{2500}\,\mathrm{hm}$	$0.0012\,\mathrm{hm}$
Kilometers	$\frac{3}{25000}\,\mathrm{km}$	$0.00012\,\mathrm{km}$
Mils (one thousandth inch)	$\frac{600000}{127}\,\mathrm{mil}$	$\approx\;4724.409449\,\mathrm{mil}$
Inches	$\frac{600}{127}\,\mathrm{in}$	$\approx\;4.724409\,\mathrm{in}$
International feet	$\frac{50}{127}\,\mathrm{ft}$	$\approx\;0.393701\,\mathrm{ft}$
International yards	$\frac{50}{381}\,\mathrm{yd}$	$\approx\;0.131234\,\mathrm{yd}$
International miles	$\frac{5}{67056}\,\mathrm{mi}$	$\approx\;0.000075\,\mathrm{mi}$
International nautical miles	$\frac{3}{46300}\,\mathrm{nmi}$	$\approx\;0.000065\,\mathrm{nmi}$
Typographic points (one seventy-second inch)	$\frac{43200}{127}\,\mathrm{pt}$	$\approx\;340.15748\,\mathrm{pt}$
Typographic picas (one sixth inch)	$\frac{3600}{127}\,\mathrm{pc}$	$\approx\;28.346457\,\mathrm{pc}$

Triangle area in all area units

Triangle solution triangle area in all area units
Unit	Exact or numerical value	Rounded view
Square nanometers	$6\times10^{14}\,\mathrm{nm}^{2}$	$600000000000000\,\mathrm{nm}^{2}$
Square micrometers	$6\times10^{8}\,\mathrm{\mu m}^{2}$	$600000000\,\mathrm{\mu m}^{2}$
Square millimeters	$600\,\mathrm{mm}^{2}$	$600\,\mathrm{mm}^{2}$
Square centimeters	$6\,\mathrm{cm}^{2}$	$6\,\mathrm{cm}^{2}$
Square decimeters	$\frac{3}{50}\,\mathrm{dm}^{2}$	$0.06\,\mathrm{dm}^{2}$
Square meters	$\frac{3}{5000}\,\mathrm{m}^{2}$	$0.0006\,\mathrm{m}^{2}$
Square decameters	$\frac{3}{500000}\,\mathrm{dam}^{2}$	$0.000006\,\mathrm{dam}^{2}$
Square hectometers	$\frac{3}{5\times10^{7}}\,\mathrm{hm}^{2}$	$6\times10^{-8}\,\mathrm{hm}^{2}$
Square kilometers	$\frac{3}{5\times10^{9}}\,\mathrm{km}^{2}$	$6\times10^{-10}\,\mathrm{km}^{2}$
Square mils (one thousandth inch)	$\frac{15\times10^{9}}{16129}\,\mathrm{mil}^{2}$	$\approx\;930001.860004\,\mathrm{mil}^{2}$
Square inches	$\frac{15000}{16129}\,\mathrm{in}^{2}$	$\approx\;0.930002\,\mathrm{in}^{2}$
Square international feet	$\frac{625}{96774}\,\mathrm{ft}^{2}$	$\approx\;0.006458\,\mathrm{ft}^{2}$
Square international yards	$\frac{625}{870966}\,\mathrm{yd}^{2}$	$\approx\;0.000718\,\mathrm{yd}^{2}$
Square international miles	$\frac{25}{107916171264}\,\mathrm{mi}^{2}$	$\approx\;2.316613\times10^{-10}\,\mathrm{mi}^{2}$
Square international nautical miles	$\frac{3}{17149520000}\,\mathrm{nmi}^{2}$	$\approx\;1.74932\times10^{-10}\,\mathrm{nmi}^{2}$
Square typographic points (one seventy-second inch)	$\frac{77760000}{16129}\,\mathrm{pt}^{2}$	$\approx\;4821.129642\,\mathrm{pt}^{2}$
Square typographic picas (one sixth inch)	$\frac{540000}{16129}\,\mathrm{pc}^{2}$	$\approx\;33.480067\,\mathrm{pc}^{2}$
International acres	$\frac{125}{843095088}\,\mathrm{acre}$	$\approx\;1.482632\times10^{-7}\,\mathrm{acre}$
Hectares	$\frac{3}{5\times10^{7}}\,\mathrm{ha}$	$6\times10^{-8}\,\mathrm{ha}$

Inputs saved with this calculation

Method: Three sides (SSS)
Active source strings: Side a: 3; Side b: 4; Side c: 5
Source unit: Centimeters
Output length unit: Centimeters
Output area unit: Square centimeters
Angle convention: degrees
Rounded decimal places: 6

What Can You Create?

Turn known measurements into a coherent triangle

Solve the case your measurements actually define

Choose the solving method from the relationships in the given problem. Three sides establish a unique shape up to reflection when all strict inequalities hold. An included angle requires a different approach from a non-included angle. The interpreted source keeps those relationships visible, while independent method buffers let you compare cases without overwriting another problem with unrelated measurements.

Recover distances and coverage from one figure

A complete solved triangle supplies coverage, perimeter, semiperimeter, perpendicular altitudes, medians, incircle radius and circumcircle radius. Side-based calculations retain exact rational and verified radical values rather than rounding an area and reusing it in later formulas. Angle-based methods identify numerical approximations honestly. The separate area-only workflow prevents an unrelated base and height from being labelled as another measurement of the same triangle.

Compare both ambiguous configurations

A non-included-angle source can describe two geometrically different triangles with identical given measurements. Inspect each branch and its opposite-side labels before applying additional practical constraints. The solver does not silently discard the supplementary inverse-sine candidate. Exported working preserves the complete solution set, while impossible or unresolved boundary cases receive a message instead of a plausible-looking invented diagram.

Triangle formulas and step-by-step examples

Check the three given sides

For $a=3\,\mathrm{cm}$ , $b=4\,\mathrm{cm}$ and $c=5\,\mathrm{cm}$ , every pair sums to more than the remaining side. The perimeter is $12\,\mathrm{cm}$ and the semiperimeter is $6\,\mathrm{cm}$ . Heron coverage is $6\,\mathrm{cm}^2$ . These exact relationships use the original source values rather than rounded intermediate measurements.

s=\frac{3+4+5}{2}=6\,\mathrm{cm},\qquad K=\sqrt{6(6-3)(6-4)(6-5)}=6\,\mathrm{cm}^{2}

Derive other distances from that same triangle

The altitude to side $c$ is $12/5\,\mathrm{cm}$ and its median is $5/2\,\mathrm{cm}$ . An altitude reaches a side line perpendicularly, while a median reaches its midpoint. The incircle radius is $1\,\mathrm{cm}$ and the circumcircle radius is $5/2\,\mathrm{cm}$ . These relationships describe different constructions even when symmetry sometimes makes their lengths equal.

h_c=\frac{2K}{c}=\frac{12}{5}\,\mathrm{cm},\quad m_c=\frac{\sqrt{2(3)^2+2(4)^2-(5)^2}}2=\frac52\,\mathrm{cm},\quad r=\frac Ks=1\,\mathrm{cm},\quad R=\frac{abc}{4K}=\frac52\,\mathrm{cm}

Distinguish included and opposite angles

Sides $b=4$ , $c=5$ and included angle $A=60^\circ$ define an SAS problem. The cosine law determines the missing side. Two known angles instead leave a third through $A+B+C=180^\circ$ , and opposite-side sine ratios then recover missing lengths. Preserve the specified side: the ASA side lies between the known angles, while the AAS side is opposite a stated known angle.

a^2=b^2+c^2-2bc\cos A=16+25-40\cos60^\circ=21,\qquad \frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}

Retain both ambiguous branches

For $a=7$ , $b=10$ and non-included angle $A=30^\circ$ , the sine ratio is $5/7$ . Both the principal candidate and its supplement leave positive third angles. With opposite side $5$ , they meet at the tangent case $B=90^\circ$ . With opposite side $4$ , the sine ratio exceeds one and no triangle satisfies the given measurements.

\sin B=\frac{10\sin30^\circ}{7}=\frac57,\qquad B_1=\arcsin\frac57,\qquad B_2=180^\circ-B_1

Separate base-height coverage and dimensions

An independent base $10\,\mathrm{cm}$ and perpendicular height $6\,\mathrm{cm}$ give $30\,\mathrm{cm}^2$ , but do not describe the default SSS triangle. The default perimeter converts to $0.12\,\mathrm{m}$ and its area to $0.0006\,\mathrm{m}^2$ . Coverage needs a squared conversion factor; applying only a length factor gives the wrong magnitude and dimension.

K_{\mathrm{base-height}}=\frac{10\cdot6}{2}=30\,\mathrm{cm}^2,\quad12\,\mathrm{cm}=0.12\,\mathrm{m},\quad6\,\mathrm{cm}^2=0.0006\,\mathrm{m}^2

Why Users Love This Tool

Why the method, precision and source labels matter

The geometry is checked before it is drawn

Strict exact inequalities separate valid SSS data from collapsed and impossible figures.
Opposite-side labels and included-angle meanings stay visible in the interpreted source.
Both SSA branches are checked, with special exact tangencies distinguished from unresolved numerical boundaries.
A base and height define coverage only, without an unsupported perimeter or unique outline.

The mathematical record remains inspectable

Rational side sources and verified radicals stay available beside separately rounded views.
Normalized numerical calculations are checked against angle sums and cosine-law residuals.
Seventeen length definitions and nineteen area definitions convert dimensions independently.
Ordered equations, source records, complete tables, sharing, CSV and PDF preserve the assumptions behind the answer.

Perfect For

Triangle reasoning for study, teaching and measured sketches

Students connecting a formula to a labelled problem

Identify the known side-angle pattern before choosing a law. Compare exact three-side working with a numerical trigonometric solution to understand which quantities depend on approximation. The default right triangle offers independently checkable area, altitude and circle-radius relationships. Ambiguous and impossible examples demonstrate why an inverse-trigonometric result is a candidate that still needs geometric filtering.

Teachers preparing complete solution comparisons

Use one source record to explain opposite-side notation, included angles and the supplementary branch in SSA. The diagram follows actual solved vertices and uses equal physical axis scales. A reflected drawing represents the same measurements. Printed working retains both valid branches, while fractional, equilateral, tangent and area-only examples provide useful contrasts without mixing unrelated geometric models.

People checking idealized flat triangular dimensions

Convert a coherent set of measured lengths into useful output units while preserving their geometric roles. Check whether a height is perpendicular and whether an angle lies between the measured sides. Practical layouts can supply an additional constraint that selects one ambiguous branch. Curved surfaces, measurement uncertainty, material thickness, allowances and purchasing increments need additional models beyond an ideal plane triangle.

How It Works

How it works in three quick steps.

Match the method to the known measurements

Choose three sides, two sides and their included angle, two angles with a stated side, or two sides and a non-included angle. Follow the opposite-side labels before entering numbers. Use base and perpendicular height only when coverage alone is defined. Select a shared source length unit and choose the angle convention explicitly.

Inspect every valid triangle and its working

Read the validity message before using a number. Strict triangle inequalities filter three-side inputs. A non-included-angle source can define no triangle, one triangle or two triangles, so inspect both valid branches. Side-based working retains verified radicals. Numerical trigonometry reports conditioning limits rather than forcing an unresolved boundary into a definite answer.

Convert dimensions and preserve the complete record

Choose independent output length and area units. Compare the solved sides, angles, perimeter, coverage, altitudes, medians and circle radii. The equal-scale drawing belongs to the inspected solution, with thin outlines omitted explicitly. Download every solution and conversion as CSV, share the active source or print both ambiguous branches to a PDF.

Download & Print

Save the complete problem and its solutions

Download every solution and conversion

CSV contains active source strings, unit choices, angle convention, every solved quantity, ordered equations and complete conversion values. Hidden conversion tables remain included, and ambiguous branches have separate solution labels. Exact squared magnitudes identify side-based radical values independently of display formatting. Preserve this record instead of copying a rounded area without its original side-angle interpretation and numerical assumptions.

Print readable mathematical working

Browser printing removes editing controls, includes both valid branches and preserves available equal-scale diagrams with their captions. Tables repeat their headings across pages and keep individual rows together. Choose a practical paper orientation when saving a PDF. Very long expressions use a visible notice pointing to the full CSV, keeping the printed record legible while complete numerical values remain downloadable.

Share one complete active problem

A shared fragment stores the selected method, its required measurements, angle convention and source/output units. Inactive editor buffers are excluded. Malformed, duplicated and extra imported fields are rejected, so another person receives a reproducible active problem. The first valid branch is inspected initially and all other branches remain available. Plain copying preserves readable mathematics for documents without a visual formula renderer.

FAQ

Frequently Asked Questions

Which measurements can solve a triangle?

The full solver supports SSS, SAS, ASA, AAS and SSA. Three sides define SSS, while SAS supplies two sides and their included angle. ASA and AAS require two angles and a clearly identified side. SSA uses a non-included angle and may have multiple outcomes. A separate base-height mode evaluates

K=bh/2

without inventing unknown sides, angles or perimeter.

Why does SSA sometimes give two answers?

The sine law gives

\sin B=b\sin A/a

. An angle and its supplement have the same sine, so both

B

and

180^\circ-B

can be candidates. Each must leave a positive third angle and recover the known side-angle relationships. The calculator considers both branches, rejects impossible configurations and retains every valid solution in copying, CSV and printing rather than silently selecting the principal inverse-sine angle.

What do the side and angle letters mean?

Side

a

is opposite angle

A

, side

b

is opposite angle

B

, and side

c

is opposite angle

C

. In SAS, known sides

b

and

c

meet at known angle

A

. ASA uses known side

c

between known angles

A

and

B

. AAS instead uses known side

a

opposite known angle

A

. These opposite-side relationships determine the problem and must be preserved when measurements are entered.

Which results are exact in SSS mode?

Finite decimal and integer-fraction sources are interpreted as rational side lengths. Perimeter, semiperimeter, Heron area, altitudes, medians and circle radii retain exact rational or verified radical expressions after conversion. Rounded views do not replace those values. All angle views use numerical inverse trigonometry, including in SSS mode. Radical simplification performs bounded work and does not promise complete factorization of an arbitrary large integer.

Why are flattened triangles and zero sides rejected?

A full nondegenerate triangle requires positive sides and strict inequalities such as

a+b>c

. Equality describes a collapsed traversal with zero coverage, for which ordinary interior-angle and circumcircle formulas no longer define a valid triangle. The solver rejects that case instead of dividing by zero or drawing an invented positive shape. Zero coverage remains available in the separate base-height mode, which makes a narrower area-only statement.

Does base-height coverage describe the SSS triangle?

Only when those measurements come from that same triangle and the height is perpendicular to the selected base line. Unrelated values must not be presented as another formula for the solved SSS figure. This tool separates base-height coverage into its own workflow. Given only

b

and

h

, the third vertex can move horizontally while coverage stays constant, so the remaining sides, angles and perimeter are not uniquely determined.

How do degrees, radians and pi-radians differ?

Choose the convention explicitly. A degree source

30

means

30^\circ

, an ordinary radian source

1/2

means half a radian, and a pi-radian source

1/6

means

\pi/6

radians. Enter only the numeric coefficient in the pi-radian field. Changing the selector reinterprets retained numbers rather than converting them. Output angles follow the chosen convention and remain numerical approximations, distinct from exact side-based quantities.

What numerical limits apply to trigonometric methods?

Known side ratios must be at least

10^{-10}

, and known angles stay at least

10^{-8}

degrees away from zero and a straight angle. Near-degenerate and unresolved SSA tangent cases report a precision limit instead of a forced answer. Exact special tangencies are identified separately. Numerical displays use at most ten decimal places, while exact SSS root views support twelve; nonzero values retain scientific views when ordinary rounding would show zero.

Why are length and area output units independent?

Perimeter and side-derived distances have the dimension of length, while coverage has the dimension of area. A length conversion factor must be squared for area:

1\,\mathrm{m}=100\,\mathrm{cm}

corresponds to

1\,\mathrm{m}^2=10000\,\mathrm{cm}^2

. Independent output selectors make that distinction explicit. The source unit interprets all known lengths together. Unitless sources are supported but receive no arbitrary physical conversion labels or tables.

Can I export and print both ambiguous solutions?

Yes. Copying and CSV preserve every valid branch, active source settings, mathematical working and all physical conversions, including visually hidden conversion tables. Printing includes both solutions and the available equal-scale diagrams while removing editing controls. Very long numerical expressions receive an explicit print notice pointing to the complete CSV. Shared links contain the active problem only, excluding unrelated inactive editing buffers and rejecting malformed or extra imported fields.

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About This Tool

About this complete triangle calculator

This triangle calculator treats geometry as a defined set of connected measurements rather than a collection of unrelated formulas. The selected method identifies which sides and angles are known and how they meet or oppose one another. Three-side, included-angle, two-angle and non-included-angle problems therefore remain separate even when some numbers happen to match. The interpreted source and opposite-side labels preserve meaning, and the validity message states whether the data defines a triangle, two possible triangles, no triangle or coverage alone.

The side-based engine interprets finite decimal and integer-fraction entries as rational values. Strict inequalities are checked before coverage is calculated, while verified radical certificates preserve derived distances and area. Numerical angle views remain separate from exact expressions. Trigonometric workflows use normalized floating-point calculations with explicit conditioning limits, and accepted solutions are checked against angle-sum and cosine-law relationships. The tool does not claim arbitrary precision for inverse trigonometry or silently force a nearly tangent case into a misleading definite answer.

Every secondary measurement belongs to the same recovered triangle, including its altitudes, medians and the radii of its incircle and circumcircle. Independent output selectors keep lengths and coverage dimensionally clear. Base-height coverage has a deliberately narrower interpretation because those two measurements cannot determine a unique perimeter or outline. The diagram, source record, ordered equations, exact or numerical labels and complete exports preserve these assumptions for learning and later inspection. Extreme numerical limits and omitted thin outlines are explained alongside the result.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Equations are checked by substituting worked examples into the stated relationship and comparing the result with the interactive implementation.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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Calculators hub

Triangle Calculator

Triangle inputs

Source, angle and output choices

Interpreted active measurements

Triangle solution: triangle area

Solved triangle diagram

Calculation step by step

Interpret the active source

Solve the selected triangle method

Read coverage and boundary separately

Derive altitudes, medians and circle radii

All triangle result details

Perimeter in all length units

Triangle area in all area units

Inputs saved with this calculation

Turn known measurements into a coherent triangle

Solve the case your measurements actually define

Recover distances and coverage from one figure

Compare both ambiguous configurations

Triangle formulas and step-by-step examples

Check the three given sides

Derive other distances from that same triangle

Distinguish included and opposite angles

Retain both ambiguous branches

Separate base-height coverage and dimensions

Why the method, precision and source labels matter

The geometry is checked before it is drawn

The mathematical record remains inspectable

Triangle reasoning for study, teaching and measured sketches

Students connecting a formula to a labelled problem

Teachers preparing complete solution comparisons

People checking idealized flat triangular dimensions

How it works in three quick steps.

Match the method to the known measurements

Inspect every valid triangle and its working

Convert dimensions and preserve the complete record

Save the complete problem and its solutions

Download every solution and conversion

Print readable mathematical working

Share one complete active problem

Frequently Asked Questions

Related calculators

Area Calculator

Pythagorean Theorem Calculator

Right Triangle Calculator

About this complete triangle calculator

Who maintains this page

Ownership and review

Methodology

Dates and sources

Explore more calculators