Pythagorean Theorem Calculator
Find any side of a right triangle given the other two. Shows step-by-step working, area, and perimeter. Enter any two sides.
Enter any two sides of the right triangle. Leave the unknown side empty.
a² + b² = c²
3
Side a
4
Side b
5
Side c (hypotenuse)
6
Area
12
Perimeter
Step-by-Step
Frequently Asked Questions
What is the Pythagorean Theorem?
The Pythagorean Theorem states that in any right-angled triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a² + b² = c².
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle. It is always opposite the right angle (90°). In the formula a² + b² = c², c represents the hypotenuse.
How do I find a missing side?
If you know sides a and b and want c: c = √(a² + b²). If you know c and one other side, say a: b = √(c² − a²). Leave the unknown field empty and enter the two known sides.
What are common Pythagorean triples?
Pythagorean triples are sets of three integers that satisfy a² + b² = c². Common examples include 3–4–5, 5–12–13, 8–15–17, and 7–24–25. Multiples of these (like 6–8–10) also work.
Where is the Pythagorean Theorem used in everyday life in Nigeria?
It is used in construction (checking that a corner is truly right-angled), surveying land boundaries, calculating diagonal distances, and in electronics for computing signal paths. It is also a core WAEC and JAMB mathematics topic.