ToolBark
Math

Pythagorean Theorem Calculator

Solve any right triangle side instantly — just enter two values

What are you solving for?

Enter Known Values

Result

Hypotenuse (c)5units
a=3b=4c=?90°
Side a (leg)3
Side b (leg)4
Side c (hypotenuse)5
Angle A (opposite a)36.8699°
Angle B (opposite b)53.1301°
Angle C (right angle)90°
Area6 sq units
Perimeter12 units
Right TriangleScalene

Step-by-Step

  1. 1Formula: c = √(a² + b²)
  2. 2Substitute: c = √(3² + 4²)
  3. 3Compute: c = √(9 + 16)
  4. 4Simplify: c = √25
  5. 5Result: c = 5

The Pythagorean Theorem

a² + b² = c²

where c is the hypotenuse (longest side, opposite the right angle)

c = √(a² + b²)

Find the hypotenuse

a = √(c² − b²)

Find leg a

b = √(c² − a²)

Find leg b

About

The Pythagorean theorem calculator lets you solve for any missing side of a right triangle using the formula a² + b² = c². Whether you need to find the hypotenuse or one of the two legs, simply enter the two known values and get an instant answer — complete with step-by-step working, all three angles, area, and perimeter. No algebra required.

FAQ
What is the Pythagorean theorem?+

The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (c) equals the sum of the squares of the two legs: a² + b² = c². It is named after the ancient Greek mathematician Pythagoras and is one of the most fundamental relationships in geometry.

How do I find the hypotenuse?+

To find the hypotenuse c, enter the lengths of both legs (a and b) and select 'Solve for c'. The calculator computes c = √(a² + b²). For example, legs of 3 and 4 give a hypotenuse of 5 (the classic 3-4-5 Pythagorean triple).

Can I solve for a leg instead of the hypotenuse?+

Yes. Select 'Solve for a' or 'Solve for b', then enter the other leg and the hypotenuse. The formula rearranges to a = √(c² − b²) or b = √(c² − a²). The hypotenuse must always be larger than either leg for a valid triangle.

What are Pythagorean triples?+

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c² exactly. Common examples include 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of a triple (e.g. 6-8-10) is also a valid Pythagorean triple.

Related tools