Geometry · 5 min read
How to Use the Pythagorean Theorem
c = √(a² + b²) — the hypotenuse of a right triangle
The Pythagorean theorem relates the three sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the two legs. This tutorial walks through the formula, a 3-4-5 worked example, and a playground that substitutes your legs into c = √(a² + b²).
Written by the My Calculator Stack editorial team. About our methods
This is a teaching diagram for a right triangle with positive legs a and b. Extreme ratios may be drawn not to scale.
1.What the theorem is
In a right triangle, one angle is 90°. The two sides that form that angle are the legs (a and b). The side opposite the right angle is the hypotenuse (c), always the longest side. The theorem says a² + b² = c². It applies only to right triangles — not to acute or obtuse ones — and the legs must be positive.
2.The formula
Solve for the hypotenuse by taking the positive square root: c = √(a² + b²). If you already know c and one leg, you can rearrange: a = √(c² − b²). The calculator on this site finds c from legs a and b.
\[ c = \sqrt{a^{2}+b^{2}} \]
3.Worked example
Take legs a = 3 and b = 4 — the same defaults as the Pythagorean theorem calculator. Then a² + b² = 9 + 16 = 25, and c = √25 = 5. That 3-4-5 triple is the classic integer right triangle. Any positive scaling (6-8-10, 1.5-2-2.5) is the same shape.
\[ c=\sqrt{3^{2}+4^{2}}=\sqrt{25}=5 \]
4.Right-triangle playground
Move the leg sliders to substitute a and b into c = √(a² + b²). The labeled triangle keeps the right angle marked; the hypotenuse label updates with c. This is a teaching widget — no favorites, no full calculator chrome. Open the Pythagorean theorem calculator when you want the standalone tool.
Inline playground
Hypotenuse c
5
c = √(3² + 4²) = 5
Teaching aid only — a and b must be positive legs of a right triangle.
Open the full Pythagorean theorem calculator →5.Open the full calculator
The Pythagorean theorem calculator uses the same c = √(a² + b²) equation and the same 3 / 4 example, with How it works, FAQ, and related geometry tools on one page. Browse other geometry calculators if you need distance, area, or circle measurements next.
Try it yourself
Open the related calculator and put these formulas to work.