Math

Triangle Area Calculator (Heron's Formula)

Enter three side lengths to find the triangle’s area, perimeter and angles.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Area
Area
—
Perimeter
—
Angle A (°)
—
Angle B (°)
—
Angle C (°)
—

Triangle Area Calculator (Heron's Formula) by TheCalcTools

How the Triangle Area Calculator (Heron's Formula) works

Enter the lengths of the three sides.

Heron’s formula uses the semi-perimeter s = (a + b + c) ÷ 2.

Angles come from the law of cosines.

The formula

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

Worked example

Using the default values shown in the calculator:

Side a3
Side b4
Side c5
  1. For a 3-4-5 triangle: s = (3 + 4 + 5) ÷ 2 = 6.
  2. Area = √(6 × 3 × 2 × 1) = 6.00.
  3. The perimeter is 12 and angle C is 90.00°.

Result:

Area6.0000
Perimeter12.0000
Angle A (°)36.87
Angle B (°)53.13
Angle C (°)90.00

Frequently asked questions

What is the triangle inequality?

The sum of any two sides must be greater than the third, otherwise the sides cannot meet to form a triangle.

When is Heron's formula useful?

When you know all three sides but not the height.

Sources and further reading

Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c² Law of Cosines CalculatorEnter two sides and the included angle (SAS) to solve the rest of the triangle Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal Trapezoid Area CalculatorEnter the two parallel sides and the height to find the area of a trapezoid

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