Triangle Calculator: Triangle Area Formula

Base and perpendicular height

A = ½ × b × h

Base b · Perpendicular height h

Start with a triangle of base b and height h, measured at a right angle to the base.

A = ½ × b × h

The two copies are congruent. Diagram not to scale for extreme proportions; use the labelled perpendicular measurements.

Start with a triangle of base b and height h, measured at a right angle to the base.

Rotate a congruent copy through half a turn to form a parallelogram with base b and perpendicular height h.

Each congruent triangle has half the parallelogram area, so A = b × h ÷ 2.

Worked example you can change

Area = base × perpendicular height ÷ 2

Editable worked example

Area = Base b × Perpendicular height h ÷ 2

Area ≈ 20 square units

Calculator

Enter complete decimal numbers using one common unit for dimensions; changing the unit label does not convert numbers. Decimal answers are shown to 15 significant digits.

Calculator inputsShape or method Unit label

Base bPerpendicular height h

Area: 20 cm²

Formula variants

Related formulas and when to use them
Shape or method	Formula	Meaning
Base and height	A = bh ÷ 2	Use the perpendicular distance to the base, not a sloping side. This mode finds area only: base and height do not determine the perimeter.
Heron’s formula	s = (a + b + c) ÷ 2; A = √(s(s − a)(s − b)(s − c))	All three sides must be positive and the longest must be shorter than the sum of the other two. Perimeter is a + b + c. A stable equivalent avoids cancellation in the area computation.

Questions

What is the triangle area formula?

Multiply the base by its perpendicular height and divide by two. A base of 8 cm and height of 5 cm give 20 cm².

Can I find triangle area with three sides?

Yes. Find semiperimeter s = (a + b + c) ÷ 2, then use Heron’s formula A = √(s(s − a)(s − b)(s − c)). Sides 3, 4 and 5 have area 6 square units.

Does this calculator solve angles or convert units?

It supports base-height and three-side area calculations, with perimeter in three-side mode. It does not solve angles. The unit selector labels dimensions without converting them.

Sources and method

Calculate triangle area from a base and perpendicular height, or use Heron’s formula from three sides. See why the area has a half factor.

We calculate with 40 significant digits and round only the displayed result. Diagrams are labelled explanations and are not measurement drawings.

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Updated 17 October 2026