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Heron's Formula Calculator

Find a triangle's area from its three sides with Heron's formula, with its angles, heights and radii.

Change the values and press Calculate to work out your own figures.

Enter the three sides.

Opposite angle A.
Opposite angle B.
Opposite angle C.
Result
Area of the triangle
666.5852815
Type
acute scalene
Side a
30
Side b
45
Side c
50
Angle A
36.33605751° = 0.6341838408 rad (36° 20′ 10″)
Angle B
62.72038726° = 1.094677266 rad (62° 43′ 13″)
Angle C
80.94355522° = 1.412731547 rad (80° 56′ 37″)
Area
666.5852815
Perimeter
125
Semiperimeter
62.5
Heights
hₐ = 44.43901877, h_b = 29.62601251, h_c = 26.66341126
Medians
mₐ = 45.13867521, m_b = 34.5506874, m_c = 28.93959226
Inradius
10.6653645
Circumradius
25.31559047
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (50, 0), C (36.25, 26.66341126)
Centroid
(28.75, 8.887803753)
Incentre
(32.5, 10.6653645)
Circumcentre
(25, 3.984861463)

The triangle's area is 666.5852815.

Show the working
  1. Three sides: each angle from the law of cosines, cos A = (b² + c² − a²) ÷ 2bc
  2. Area = √(s(s − a)(s − b)(s − c)) = 666.5852815

How to use it

Enter the three sides.

Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.

Key facts

A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Why it works

Heron's formula needs no angles or heights: the three sides determine the triangle completely.

Questions

What is the area of a 3-4-5 triangle?

6.

What is s?

The semiperimeter, half the perimeter.

Reviewed by RK Calculator Team. Updated 2026-09-26.

Formulas

A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Sources

Limitations

  • Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).

Formula version 0.1.0Reviewed