mathematics calculator
3 Sides Triangle Area Calculator
Find a triangle's area from three known side lengths using Heron's formula.
3 Sides Triangle Area Calculator
Triangle area
Enter all three side lengths.
Use the same unit for all sides. The area is returned in that unit squared.
Formula version 1.0.0
How to use this calculator
- Enter all three positive side lengths in one unit.
- Confirm each pair sums to more than the remaining side.
- Select Calculate.
- Read area and semiperimeter from Heron's formula.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
a,b,c | Triangle side lengths | length |
s | Semiperimeter (a+b+c)/2 | length |
A | Triangle area | square length |
Checked examples
3-4-5 triangle
Inputs: Sides 3, 4, 5
Calculation: s=6; A=√[6(6−3)(6−4)(6−5)]
Result: 6 square units
The familiar right triangle has base-height area six.
Check: triangle-three-sides.test.ts
Equilateral triangle
Inputs: Sides 2, 2, 2
Calculation: s=3; A=√(3×1×1×1)
Result: √3 square units
All three equal sides form a valid equilateral triangle.
Check: triangle-three-sides.test.ts
Assumptions, rounding, and limits
- All sides are positive and share one unit.
- Strict triangle inequalities hold.
- The triangle is Euclidean and planar.
- Displayed rounding does not alter internal precision.
Frequently asked questions
Why is 1, 2, 3 rejected?
Those lengths form a straight degenerate shape, not a triangle with positive area.
Do I need an angle?
No. Three valid sides determine the area through Heron's formula.
What unit is the answer?
The square of the common side-length unit.
Sources and review
- OpenStax: Non-right Triangles: Law of Cosines — Heron's formula
- Formula version
- triangle.three-sides@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Planar Euclidean triangle area from three valid sides.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
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