Right Triangle Calculator

Right triangle calculator: enter any 2 values

This free right triangle calculator solves any right triangle from just two known values. Enter any two of the legs, hypotenuse, angles, altitude, area, or perimeter, and it instantly returns every side, both acute angles, the area, and more. It starts with the classic 3-4-5 triangle in feet, the builder's check for a square corner.

How to use the right triangle calculator

1. Type any two known values into the form: two sides, a side and an angle, or a combination with the area, perimeter, or altitude.
2. Pick your unit (mm, cm, m, km, in, ft, yd, or mi, or no unit) and choose whether angles are in degrees or radians.
3. Read the results: all three sides, both acute angles, the area, perimeter, altitude, inradius, and circumradius.
4. Check the step-by-step solution and the scaled diagram, then copy the shareable link to save or send your answer.

Results update as you type, and Pythagorean triples and special right triangles are labeled automatically. Measuring with a tape? The right triangle calculator in feet and inches takes readings like 5' 6 3/8" and gives every side to the nearest 1/16 in.

Area of a right triangle calculator

Finding the area of a right triangle is easier than for any other triangle, because the two legs are already perpendicular. One leg is the base and the other is the height, so the formula is simply:

Area = ½ × a × b

For example, a right triangle with legs of 6 ft and 8 ft has an area of ½ × 6 × 8 = 24 ft². Area is always measured in square units (cm², m², in², ft², and so on), and the calculator converts it for you when you switch units.

Area of a right triangle without both legs

• Hypotenuse and one leg: find the other leg with b = √(c² − a²), then use ½ × a × b.
• Hypotenuse and one angle: Area = ½ × c² × sin α × cos α.
• One leg and one angle: b = a / tan α, so Area = a² / (2 × tan α).
• Hypotenuse and altitude: Area = ½ × c × h, where h is the height drawn to the hypotenuse.

You don't need to memorize these. Enter what you know into the area of a right triangle calculator above and it picks the right formula. It also works in reverse: enter the area and one side to find the missing side. See also the right triangle formulas reference.

Right triangle calculator with angles

The calculator works just as well with angles as with sides. When you know one acute angle and one side, the trigonometric ratios (SOH-CAH-TOA) give you everything else:

• sin α = opposite / hypotenuse = a / c
• cos α = adjacent / hypotenuse = b / c
• tan α = opposite / adjacent = a / b

To find the angles from two sides, the calculator runs those ratios backwards: α = arctan(a / b), or α = arcsin(a / c) when you know the hypotenuse. The second angle is then β = 90° − α, because the two acute angles of every right triangle add up to 90°.

Angles can be in degrees or radians. An angle alone can't fix a triangle's size, so pair it with a side, the area, or the perimeter.

What is a right triangle?

A right triangle (or right-angled triangle) is a triangle with one angle of exactly 90°. The side opposite the right angle is the hypotenuse, and it is always the longest side. The two sides that form the right angle are the legs. Because a triangle's angles add up to 180°, the other two angles must add up to 90°.

Here, legs a and b sit opposite angles α and β, and c is the hypotenuse. The sides are linked by the Pythagorean theorem, a² + b² = c². If you only need a missing side, use the Pythagorean theorem calculator.

Worked example: squaring a corner with the 3-4-5 rule

Builders check that a corner is square with the 3-4-5 rule: mark 3 ft along one wall and 4 ft along the other, then measure between the marks. If the diagonal is exactly 5 ft, the corner is a true 90°. That's the triangle the calculator starts with. The hypotenuse is c = √(3² + 4²) = √25 = 5 ft. The area is ½ × 3 × 4 = 6 ft², and the perimeter is 3 + 4 + 5 = 12 ft. The angles are α = arctan(3/4) ≈ 36.87° and β = 90° − 36.87° = 53.13°. The altitude to the hypotenuse is h = (3 × 4)/5 = 2.4 ft, the inradius is (3 + 4 − 5)/2 = 1 ft, and the circumradius is 5/2 = 2.5 ft.

Because 3-4-5 is a Pythagorean triple (three whole numbers with a² + b² = c²), the calculator flags it, as it does for scaled copies like 6-8-10. For a large layout such as a deck or a foundation, builders use one of those copies, 6-8-10 or 9-12-15, because a small error shows up more clearly on a bigger triangle. If the diagonal comes out longer than 5 ft, the corner is wider than 90°; if it's shorter, the corner is tighter. To size the triangle for your own layout and check a whole frame by its diagonals, use the 3-4-5 rule calculator. To cut a brace that keeps a gate or frame square, the diagonal brace calculator gives its length and the angle at each end.

Special right triangles

Two right triangles have fixed side ratios, so you can solve them from a single side. The 45-45-90 triangle is an isosceles right triangle with sides in the ratio 1 : 1 : √2. The 30-60-90 triangle has sides in the ratio 1 : √3 : 2. Use the special right triangle calculator to solve either one, or go straight to the 30-60-90 triangle calculator or the isosceles right triangle calculator.

Key definitions

Leg

One of the two shorter sides that form the right angle, called a and b here.

Hypotenuse

The side opposite the right angle and the longest side of a right triangle, called c here.

Altitude to the hypotenuse

The perpendicular line from the right angle to the hypotenuse. Its length is (a × b)/c.

Right triangle calculator FAQ

More questions? See the full right triangle FAQ.

Cite this page

To cite this calculator in schoolwork or a report, you can use this reference (APA style):

Right Triangle Calculators. (2026, October 10). Right triangle calculator. https://righttrianglecalculators.com/

References

The formulas and definitions on this page match these standard references.

1. Weisstein, Eric W. “Right Triangle.” MathWorld, Wolfram Research.
2. Weisstein, Eric W. “Pythagorean Theorem.” MathWorld, Wolfram Research.
3. “§4.14 Definitions and Periodicity (Trigonometric Functions).” NIST Digital Library of Mathematical Functions, National Institute of Standards and Technology.