Right Triangle Calculator
Enter two perpendicular legs to calculate hypotenuse, area, perimeter, acute angles, sine, cosine, tangent, and converted length or area units.
Inputs
2 Legs
Angles
Both Acute Angles
Ratios
sin, cos, tan
Live calculator
Right triangle inputs
Enter perpendicular legs to calculate hypotenuse, area, perimeter, acute angles, and basic trig ratios.
Hypotenuse
5 cm
Area
6 cm²
Perimeter
12 cm
Angle A
36.8699 deg
Angle B
53.1301 deg
Hypotenuse in other units
| Unit | Converted value | Meaning |
|---|---|---|
| nm | 50,000,000 | Nanometers |
| um | 50,000 | Micrometers |
| mm | 50 | Millimeters |
| cm | 5 | Centimeters |
| dm | 0.5 | Decimeters |
| m | 0.05 | Meters |
| dam | 0.005 | Decameters |
| hm | 0.0005 | Hectometers |
| km | 0.0001 | Kilometers |
| mil | 1,968.5039 | Mils |
| in | 1.9685 | Inches |
| ft | 0.164 | Feet |
| yd | 0.0547 | Yards |
| mi | 0 | Miles |
| nmi | 0 | Nautical miles |
| pt | 141.7323 | Points |
| pc | 11.811 | Picas |
Area in other units
| Unit | Converted value | Meaning |
|---|---|---|
| nm² | 600,000,000,000,000 | Square nanometers |
| um² | 600,000,000 | Square micrometers |
| mm² | 600 | Square millimeters |
| cm² | 6 | Square centimeters |
| dm² | 0.06 | Square decimeters |
| m² | 0.0006 | Square meters |
| dam² | 0 | Square decameters |
| hm² | 0 | Square hectometers |
| km² | 0 | Square kilometers |
| mil² | 930,001.86 | Square mils |
| in² | 0.93 | Square inches |
| ft² | 0.0065 | Square feet |
| yd² | 0.0007 | Square yards |
| mi² | 0 | Square miles |
| nmi² | 0 | Square nautical miles |
| pt² | 4,821.1296 | Square points |
| pc² | 33.4801 | Square picas |
Trig ratios for angle A
sin A
0.6
cos A
0.8
tan A
0.75
Inputs
2 Legs
Angles
Both Acute Angles
Ratios
sin, cos, tan
Calculate right-triangle measurements
Side lengths
Find the hypotenuse from the two perpendicular legs using the Pythagorean theorem.
Area and perimeter
Calculate one-half leg product for area and add all sides for perimeter.
Angles and ratios
Connect side ratios to acute angles, sine, cosine, and tangent.
Right triangle formulas used on this page
The calculator uses leg lengths to calculate geometry values and basic trigonometry ratios.
Working formulas
Hypotenuse
c = sqrt(a^2 + b^2)
The hypotenuse is opposite the right angle.
Area
A = (a x b) / 2
The perpendicular legs act as base and height.
Tangent
tan(A) = opposite / adjacent
For angle A, this page treats leg a as opposite and leg b as adjacent.
Symbols
- a, b - legs
- The two sides that meet at the right angle.
- c - hypotenuse
- The longest side, opposite the 90 degree angle.
- A - acute angle
- One non-right angle used for sine, cosine, and tangent ratios.
Right-triangle outputs that connect geometry to trig
Formula-backed trig basics
- The calculator starts with the values users already know before moving into lesson notes.
- Results keep squared terms, side labels, angles, and trig ratios visible for checking.
- Inputs support decimal measurements for practical right-triangle and layout problems.
- Copy and print controls help students and teachers move results into notes or worksheets.
Right-triangle guardrails
- Missing-leg calculations require the hypotenuse to be longer than the known leg.
- Angle outputs are calculated from the leg ratio and displayed in degrees for classroom readability.
- Related links connect theorem, right-triangle, unit-circle, converter, and guide content.
- FAQ sections explain common mistakes such as mixing legs with hypotenuse or mixing degrees with radians.
Right-triangle support for formulas and lessons
Students
Check right-triangle homework while seeing the formula path that produced the result.
Teachers
Create examples for theorem lessons, trigonometry introductions, and unit circle prep.
Worksheet builders
Print results and supporting notes for answer keys, examples, and review sheets.
How it works in three quick steps.
Enter leg a and leg b
Use the two sides that meet at the right angle.
Read side and area results
Use the hypotenuse, perimeter, and area outputs for geometry checks.
Review angles and trig ratios
Use acute angle and sine, cosine, tangent outputs to connect geometry to trigonometry.
Save or print right-triangle calculations
Copy the result
Copy sides, angles, formulas, and output values into notes or lesson documents.
Print the page
Print calculator inputs, result cards, formulas, FAQs, and related links.
Compare values
Change one side length at a time to see how hypotenuse, area, and angles respond.
Frequently Asked Questions
What inputs does the right triangle calculator need?
How are the acute angles calculated?
What do sine, cosine, and tangent mean here?
Can this solve non-right triangles?
Why is area one-half leg a times leg b?
Related trigonometry tools
About this right triangle calculator
Toolarithm's Right Triangle Calculator builds on the Pythagorean theorem and introduces the side ratios used in trigonometry. With two perpendicular legs, it calculates the hypotenuse, area, perimeter, acute angles, sine, cosine, and tangent. The calculator is intentionally focused on right triangles so the assumptions stay clear.
The page is useful as a bridge between geometry and trigonometry. Students can see how side lengths create a hypotenuse, how the same legs form area, and how ratios become angle relationships. Unit tables separate linear outputs from square-unit area outputs, while related links connect the calculator to the Pythagorean theorem, unit circle values, and degrees-to-radians conversion.
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 methodologyDates and sources
Review dates change only after a substantive method or content check.
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