Pythagoras Calculator
Pythagoras Calculator works out Leg a and Leg b from Leg a (opposite angle A), Leg b (opposite angle B) and Hypotenuse c. The default figures on this page give hypotenuse c of 5; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Pythagoras: a^2 + b^2 = c^2, so 3^2 + 4^2 = 9 + 16 = 25 and c = sqrt(25) = 5.
- Solved from two legs (Pythagoras).
- Legs a = 3, b = 4; hypotenuse c = sqrt(a^2 + b^2) = 5.
- Angle A = arctan(a/b) = 36.86989764584402 deg, angle B = 90 - A = 53.13010235415598 deg.
- Area = a*b/2 = 6; perimeter = a + b + c = 12.
- Altitude to the hypotenuse = a*b/c = 2.4; the right angle's vertex projects onto the hypotenuse dividing it into a^2/c and b^2/c.
Its 10 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the Pythagoras Calculator calculates
Solves a right triangle from any two of leg a, leg b, hypotenuse, an acute angle, the area or the perimeter, returning all sides, angles, area, altitude to the hypotenuse, inradius and circumradius.
How to use this Pythagoras Calculator
Enter Leg a (opposite angle A), Leg b (opposite angle B), Hypotenuse c and Angle unit. Leg a updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Leg a, Leg b and Hypotenuse c.
The method follows Euclid, Elements, Book I Proposition 47 (the Pythagorean theorem), NIST Digital Library of Mathematical Functions, 4.14 Definitions and periodicity (right-triangle ratios), Weisstein, Eric W. "Right Triangle", MathWorld and OSHA 29 CFR 1926.1053(b)(5)(i) — non-self-supporting ladders are set with the base about one quarter of the working length from the support.
What you can compare
Change one input at a time to see how it affects Leg a, Leg b and Hypotenuse c. The inputs you can vary are Leg a (opposite angle A), Leg b (opposite angle B), Hypotenuse c and Angle unit.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
What is the full Pythagoras formula?
On the figures this page opens with — leg a (opposite angle A) 3 and leg b (opposite angle B) 4 — the hypotenuse c is 5. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
What are the two formulas for Pythagoras?
It needs Leg a (opposite angle A), Leg b (opposite angle B), Hypotenuse c and Angle unit. Nothing else is required, and the figures stay in your browser.
What is Pythagoras in maths?
Solves a right triangle from any two of leg a, leg b, hypotenuse, an acute angle, the area or the perimeter, returning all sides, angles, area, altitude to the hypotenuse, inradius and circumradius. On this page it is computed from Leg a (opposite angle A), Leg b (opposite angle B) and Hypotenuse c and shown as Leg a, Leg b and Hypotenuse c.
What information do I need for the Pythagoras Calculator?
You need Leg a (opposite angle A), Leg b (opposite angle B), Hypotenuse c and Angle unit. The page opens with default figures that give hypotenuse c of 5, so you can see the scale before entering your own.
What does this Pythagoras Calculator show?
It shows Leg a, Leg b, Hypotenuse c, Angle A, Angle B, Angle C (right angle), Angle A in degrees and Angle A in radians, with the working and any warnings for your entries.
Can I check how the Pythagoras Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.