Which side is the hypotenuse?

The hypotenuse is the side opposite the right angle. It is always the longest side of a right triangle.

Can I find an angle as well as a side?

Yes. After the missing side is found, the calculator uses inverse trigonometry to show both acute angles.

Can I use feet and inches?

Use decimal feet or convert inches to the same unit before entering the two known sides.

How do I find the missing side of a right triangle?

Identify the hypotenuse first, enter the two known sides, and rearrange a² + b² = c². The calculator chooses the matching square-root formula.

Can I share a calculation?

Yes. Use Share to copy a URL containing the current calculator values, then open that link on another device or send it to someone else.

Pythagorean Theorem Calculator – Find Sides & Angles

A clear answer before the details

For a right triangle, a² + b² = c². The hypotenuse c is opposite the right angle and must be longer than either leg.

A right triangle calculator for finding a, b, or c

The Pythagorean theorem calculator works only for a right triangle, where one angle is 90°. The two shorter sides are the legs a and b, and the longest side opposite the right angle is the hypotenuse c. Choose find a, find b, or find c, enter the two known sides, and the result shows the square-root rearrangement. The right triangle calculator also estimates the two acute angles so you can check the geometry.

Using consistent units and checking the theorem

A Pythagorean calculator with feet and inches needs consistent measurements. Convert inches to decimal feet, or convert every dimension to inches before calculating; do not mix 6 feet with 8 inches as if both were the same unit. After solving, verify a² + b² = c² and confirm that c is longer than either leg. This makes the tool useful for ramps, ladders, diagonals, coordinate distances, and classroom geometry.

Formula guide

The key equations are separated below. Start with the calculator mode, then choose the shape or model that matches your problem.

Pythagorean theorem

a² + b² = c²

c is the hypotenuse opposite the right angle.

Find the hypotenuse

c = √(a² + b²)

Use this when both legs are known.

Find a missing leg

a = √(c² − b²)

The hypotenuse must be longer than the known leg.

Find the other leg

b = √(c² − a²)

Use this when leg a and hypotenuse c are known.

Acute angles

A = sin⁻¹(a/c), B = sin⁻¹(b/c)

The calculator also reports both acute angles in degrees.

Worked example

With legs 3 and 4, c = √(3² + 4²) = √25 = 5. The acute angles are approximately 36.87° and 53.13°.

Formulas for common use cases

Use the matching equation for the problem you are solving, then enter its variables in the calculator above.

Ramps and ladders

diagonal = √(rise² + run²)

Treat the rise and run as the two legs of a right triangle.

Coordinate distance

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Horizontal and vertical changes form the legs.

Check a right triangle

largest side² = other side² + other side²

A true right triangle satisfies the theorem.

How to use this calculator

Select the side you want to find.
Enter the two known positive sides.
Check that a valid right triangle is possible.
Read the missing side, radical form when exact, and angles.

Where it helps

This right-triangle calculator helps with classroom exercises, construction layouts, ramps, ladders, coordinate geometry, and distance problems. A diagram keeps the roles of the legs and hypotenuse clear, and the angle results make the page useful for trigonometry practice as well as the theorem itself.

Common mistakes

The hypotenuse is never one of the legs and must be the longest side. If you solve for a leg, the known hypotenuse must exceed the other leg. Do not use the theorem for a triangle without a right angle; general triangles require a different rule such as the law of cosines.