Plane geometry

Triangle Calculator

Find a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality.

Explicit formulas and worked examples
Check your inputs, then calculate
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Check the stated input format, calculation convention and limits before using the result.

Check the example inputs, then calculate. Your values stay in this browser.

Area is in squared units; perimeter is in the entered length unit.

Calculation notes

Understand the Triangle Calculator

Triangle Calculator validates first side, second side, third side before applying the displayed equation. Area is in squared units; perimeter is in the entered length unit.

Formula and logic

What is the formula for the Triangle Calculator?

Triangle Calculator: s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)); perimeter = a+b+c. Input definitions: a = First side; b = Second side; c = Third side. Use the selected convention throughout the calculation.

Worked example

How can I reproduce the Triangle Calculator example?

Triangle Calculator baseline input: First side: 3; Second side: 4; Third side: 5. Output: Area (Heron) = 6; Perimeter = 12. Substitute these values into the displayed equation to reproduce the result.

How to read the result

How should I interpret the Triangle Calculator result?

Read area (heron) with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.

Limits and assumptions

What limits apply to the Triangle Calculator?

Area is in squared units; perimeter is in the entered length unit.
Degenerate triangles and zero-length sides are rejected.

Content and calculation reviewed: 2026-10-11

Understand the calculation

How to use it and the math behind it

Read the complete explanation

Four steps to check your inputs and results

Find a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality.
Enter First side, Second side, Third side in the stated format. Baseline values are for reproduction.
Check the output unit and convention: Read area (heron) with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input and compare the result. Area is in squared units; perimeter is in the entered length unit. Degenerate triangles and zero-length sides are rejected.