What is the formula for the area of a right triangle?

The area of a right triangle is calculated using the formula Area = ½ × base × height, where the base and height are the two legs that meet at the right angle (90°). For example, a right triangle with a base of 6 and a height of 8 has an area of ½ × 6 × 8 = 24 square units.

How do I find the hypotenuse of a right triangle?

The hypotenuse is the longest side of a right triangle, opposite the right angle. You find it using the Pythagorean theorem: hypotenuse = √(base² + height²). For a triangle with base 6 and height 8, the hypotenuse is √(36 + 64) = √100 = 10.

What are the angles in a right triangle?

Every right triangle has one angle of exactly 90° (the right angle) and two acute angles that together sum to 90°. The angle adjacent to the base is calculated as arctan(height ÷ base), and the angle adjacent to the height is arctan(base ÷ height). All three angles always add up to 180°.

Area of a Right Triangle Calculator

Enter the base and height of a right triangle, the two legs that meet at the right angle, to instantly calculate its area, hypotenuse, perimeter, and all three interior angles, with a worked example shown below.

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Standard formula Area = ½ × base × height. Hypotenuse via Pythagorean theorem.

1. Triangle Dimensions

Base (leg a) horizontal leg, adjacent to right angle

units

Please enter a positive number.

Height (leg b) vertical leg, adjacent to right angle

units

Please enter a positive number.

Unit label optional, for display only

2. Quick Reference

A right triangle has one angle of exactly 90°. The two shorter sides (legs) are called the base and height. The longest side, opposite the right angle, is the hypotenuse.

Formulae used:
Area = ½ × base × height
Hypotenuse = √(base² + height²)
Angle A = arctan(height ÷ base)
Angle B = arctan(base ÷ height)
Perimeter = base + height + hypotenuse

Results

Area
24
units²

Hypotenuse

10.00

units

Perimeter

24.00

units

Angle A (at base)

53.13°

Opposite to height

Full Measurements

Base (leg a)6 units

Height (leg b)8 units

Hypotenuse (leg c)10.00 units

Perimeter24.00 units

Area24.00 units²

All Angles

Right angle (C)90.00°

Angle A (opposite height)53.13°

Angle B (opposite base)36.87°

Sum of angles180.00°

Area formula½ × 6 × 8 = 24

Worked Example (default values)

Given: base = 6 units, height = 8 units

Area = ½ × 6 × 8 = 24 units²

Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10.00 units

Perimeter = 6 + 8 + 10 = 24.00 units

Angle A = arctan(8 ÷ 6) = arctan(1.3333) = 53.13°

Angle B = 90° − 53.13° = 36.87°

How to Calculate the Area of a Right Triangle

A right triangle (also called a right-angled triangle) is a triangle with one interior angle equal to exactly 90°. The two sides that form the right angle are called the legs (or base and height). The side opposite the right angle is the hypotenuse, which is always the longest side.

The area formula is straightforward: multiply the two legs together and divide by two. This works because a right triangle is exactly half of a rectangle with the same base and height.

Measurement	Formula	Example (base=6, height=8)
Area	½ × base × height	½ × 6 × 8 = 24 units²
Hypotenuse	√(base² + height²)	√(36 + 64) = 10 units
Perimeter	base + height + hypotenuse	6 + 8 + 10 = 24 units
Angle A (at base)	arctan(height ÷ base)	arctan(8÷6) = 53.13°
Angle B (at height)	arctan(base ÷ height)	arctan(6÷8) = 36.87°

The Pythagorean Theorem

The Pythagorean theorem states that in any right triangle: a² + b² = c², where a and b are the legs and c is the hypotenuse. This is one of the most fundamental relationships in geometry. The 3-4-5 triangle is the simplest Pythagorean triple with integer sides: 3² + 4² = 9 + 16 = 25 = 5². The default example in this calculator (6, 8, 10) is a scaled version of the 3-4-5 triple.

Common Right Triangle Applications

Right triangles appear throughout everyday life and practical tasks:

Building and construction: checking that walls and floors are square (the 3-4-5 rule), calculating roof pitch, and working out rafter lengths.
Land surveying: measuring plots and calculating areas where survey lines meet at right angles.
Navigation: calculating straight-line distance when you know north-south and east-west displacements.
Screen and display sizing: diagonal measurement of screens from width and height.
Physics and engineering: resolving forces, vector components, and inclined planes.

Special Right Triangles

Two right triangles have especially useful angle ratios:

45-45-90 triangle: both legs are equal, and the hypotenuse is leg × √2. For example, a triangle with legs of 5 has a hypotenuse of 5√2 ≈ 7.07.
30-60-90 triangle: the short leg is half the hypotenuse, and the long leg is short leg × √3. These occur when you cut an equilateral triangle in half.

Related Calculators

Maths and Stats Calculators: all geometry and statistics tools.
Area of a Triangle Calculator: any triangle using base and height or two sides and an angle.
Area of a Triangle using Heron's Formula: area from three side lengths.
Pythagorean Theorem Calculator: find any missing side of a right triangle.
Area of a Circle Calculator: area and circumference from radius or diameter.

Method: Area = ½ × base × height (standard formula for a right triangle). Hypotenuse calculated using the Pythagorean theorem: c = √(a² + b²). Angles calculated using inverse tangent (arctan). All calculations are performed in the browser and are exact to floating-point precision.

Results are mathematically exact for the values entered. Ensure your base and height are in the same units before using this calculator.

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