Triangle Area Calculator
Calculate a triangle’s area from its three side lengths using Heron’s formula.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
Area (u²)
About this calculator
Enter three positive side lengths in the same unit. Length results use that input unit (u), and area uses its square (u²); this calculator does not choose or convert a measurement unit.
Worked example
calculated with the default values below
Side A 3 u · Side B 4 u · Side C 5 u Area 6.0000 u² · Perimeter 12.0000 u · Semi-perimeter 6.0000 u · Right-angle test (1 = yes) 1
Method and assumptions
Formula basis and scope
s = (a + b + c)/2; area = sqrt(s(s - a)(s - b)(s - c)).
All sides must be positive and satisfy the strict triangle inequality.
Data sources
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
A = √(p(p−a)(p−b)(p−c)); p = (a+b+c) ÷ 2
- a,b,c
- Side lengths
- p
- Semiperimeter
- A
- Area
Enter three positive side lengths in the same arbitrary unit u; lengths are in u and area in u². No unit is selected or converted.
Frequently asked questions
How is area calculated from three sides?
Enter three positive side lengths in the same unit that satisfy the triangle inequality: any two must add to more than the third. The calculator uses Heron’s formula. For example, sides 3, 4 and 5 have an area of 6 square units and form a right triangle.
Can I enter a base and height instead?
No. This page accepts three side lengths only. It does not have base or height inputs; use a calculator that supports that input method if those are the measurements you have.