Pythagorean Theorem Calculator
Find the missing side of a right triangle using the Pythagorean theorem.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
Hypotenuse c (cm)
About this calculator
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. Enter any two sides and the third follows immediately.
Worked example
calculated with the default values below
Side a 3 cm · Side b 4 cm · Hypotenuse c (leave 0 to solve for it) 0 cm Hypotenuse c 5.0000 cm · Side a 3.0000 cm · Side b 4.0000 cm · Area 6.0000 cm² · Perimeter 12.0000 cm
Method and assumptions
c = √(a² + b²); b = √(c² − a²); S = a×b÷2; P = a+b+c Enter exactly two positive side lengths; leave the unknown side at zero. The hypotenuse must exceed either leg. In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. Enter any two sides and the third follows immediately. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Data sources
The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
c = √(a² + b²); b = √(c² − a²); S = a×b÷2; P = a+b+c
- a
- Leg a
- b
- Leg b
- c
- Hypotenuse c
- S
- Area
- P
- Perimeter
Enter exactly two positive side lengths; leave the unknown side at zero. The hypotenuse must exceed either leg.
Frequently asked questions
How many sides should I enter?
Enter exactly two positive side lengths and leave the unknown side at 0. If you enter the hypotenuse c and one leg, c must be longer than that leg; otherwise the measurements are impossible and the calculator reports an error.
Which inputs and limits apply to Pythagorean Theorem Calculator?
Use the units shown beside each field. These are form limits, not recommended settings. Side a: 0–1,000,000,000 cm; Side b: 0–1,000,000,000 cm; Hypotenuse c (leave 0 to solve for it): 0–1,000,000,000 cm c = √(a² + b²); b = √(c² − a²); S = a×b÷2; P = a+b+c Enter exactly two positive side lengths; leave the unknown side at zero. The hypotenuse must exceed either leg. In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. Enter any two sides and the third follows immediately. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
What is a complete worked example for Side a = 3 cm; Side b = 4 cm?
Inputs: Side a = 3 cm; Side b = 4 cm; Hypotenuse c (leave 0 to solve for it) = 0 cm. Calculation: c = √(a² + b²); b = √(c² − a²); S = a×b÷2; P = a+b+c. Results: Hypotenuse c = 5.0000 cm; Side a = 3.0000 cm; Side b = 4.0000 cm; Area = 6.0000 cm²; Perimeter = 12.0000 cm.