Triangle Calculator
Check triangle side validity and calculate perimeter, semiperimeter, Heron's formula area, base-height area, and converted units from one live calculator.
Checks
Triangle Inequality
Area Modes
Heron + Base Height
Classification
Side Type
Live calculator
Triangle formula inputs
Check side validity, perimeter, semiperimeter, Heron area, and base-height area.
Heron area
14.696938 cm²
Perimeter
18 cm
Semiperimeter
9 cm
Base-height area
30 cm²
Type
scalene
Perimeter in other units
Scroll horizontally inside this table to view every column on smaller screens.
| Unit | Converted value | Meaning |
|---|---|---|
| nm | 180,000,000 | Nanometers |
| um | 180,000 | Micrometers |
| mm | 180 | Millimeters |
| cm | 18 | Centimeters |
| dm | 1.8 | Decimeters |
| m | 0.18 | Meters |
| dam | 0.018 | Decameters |
| hm | 0.0018 | Hectometers |
| km | 0.0002 | Kilometers |
| mil | 7,086.6142 | Mils |
| in | 7.0866 | Inches |
| ft | 0.5906 | Feet |
| yd | 0.1969 | Yards |
| mi | 0.0001 | Miles |
| nmi | 0.0001 | Nautical miles |
| pt | 510.2362 | Points |
| pc | 42.5197 | Picas |
Base-height area in other units
Scroll horizontally inside this table to view every column on smaller screens.
| Unit | Converted value | Meaning |
|---|---|---|
| nm² | 3,000,000,000,000,000 | Square nanometers |
| um² | 3,000,000,000 | Square micrometers |
| mm² | 3,000 | Square millimeters |
| cm² | 30 | Square centimeters |
| dm² | 0.3 | Square decimeters |
| m² | 0.003 | Square meters |
| dam² | 0 | Square decameters |
| hm² | 0 | Square hectometers |
| km² | 0 | Square kilometers |
| mil² | 4,650,009.3 | Square mils |
| in² | 4.65 | Square inches |
| ft² | 0.0323 | Square feet |
| yd² | 0.0036 | Square yards |
| mi² | 0 | Square miles |
| nmi² | 0 | Square nautical miles |
| pt² | 24,105.6482 | Square points |
| pc² | 167.4003 | Square picas |
Triangle inequality
A valid triangle needs each pair of sides to add up to more than the remaining side. The calculator labels invalid side sets before using Heron's formula.
Checks
Triangle Inequality
Area Modes
Heron + Base Height
Classification
Side Type
Calculate triangle measurements and validity
Side validity
Check whether three side lengths pass the triangle inequality before using side-based formulas.
Perimeter
Add all three side lengths and calculate semiperimeter for Heron's formula.
Two area methods
Compare Heron's formula from sides with one-half base times perpendicular height.
Triangle formulas used on this page
Triangle calculations depend on whether you know three sides or a base with perpendicular height.
Working formulas
Perimeter
P = a + b + c
Add the three side lengths.
Semiperimeter
s = P / 2
Heron's formula starts with half the perimeter.
Heron's formula
A = sqrt(s(s-a)(s-b)(s-c))
Use only when the three sides form a valid triangle.
Base-height area
A = (base x height) / 2
Height must be perpendicular to the chosen base.
Symbols
- a, b, c - side lengths
- The three edges of the triangle used for perimeter and Heron's formula.
- s - semiperimeter
- Half of the perimeter, used inside Heron's formula.
- h - height
- The perpendicular distance from the base to the opposite vertex.
Triangle outputs with validity checks
Formula-backed results
- The live calculator appears first so users can enter dimensions before reading long explanations.
- Each result stays connected to a visible formula instead of returning a bare number.
- Inputs accept decimals for measurement problems that do not use whole-number dimensions.
- Copy and print controls help users move results into notes, worksheets, and classroom examples.
Geometry guardrails
- Invalid triangle side sets are labeled clearly before Heron's formula is used.
- Circle calculations use radius consistently so diameter, area, circumference, sectors, and arcs agree.
- Shape labels separate area from perimeter so users do not confuse surface coverage with edge length.
- Related links connect the calculator page to the geometry hub and printable formula reference.
Triangle support for geometry practice
Students
Check homework dimensions while keeping the formula and unit meaning visible.
Teachers
Create quick examples for geometry worksheets, board notes, and answer keys.
Printable work
Print the page with inputs, results, formulas, FAQs, and related geometry links.
How it works in three quick steps.
Enter three side lengths
Use side A, side B, and side C to calculate perimeter and validate the triangle.
Enter base and height
Use perpendicular height with the chosen base for the base-height area formula.
Compare area methods
Use Heron's formula when three valid sides are known, or base-height area when height is known.
Save or print triangle calculations
Copy the result
Copy the calculated measurements and formula context into notes or lesson drafts.
Print the page
Print the calculator result with formula explanations and FAQ support below it.
Compare nearby values
Change one dimension at a time to see how the measurement responds.
Frequently Asked Questions
What does the triangle calculator check first?
When should I use Heron's formula?
When should I use base times height divided by two?
How does the calculator classify triangle type?
Why can Heron area and base-height area be different?
Related geometry tools
About this triangle calculator
Toolarithm's Triangle Calculator handles the two most common triangle workflows: side-based calculations and base-height area. The side fields calculate perimeter, semiperimeter, triangle validity, side classification, and Heron's formula area. The base and height fields calculate the familiar one-half base times height area formula.
The calculator is careful about validity because not every group of three positive numbers can become a triangle. If one side is too long compared with the other two, the side set is invalid. That matters because Heron's formula assumes a real triangle. Use the unit selector when triangle dimensions come from a drawing scale, worksheet, construction sketch, or map. The side results stay in the selected linear unit, while Heron and base-height area results are displayed in square units.
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.
Keep building