Hypotenuse Calculator
Find a right triangle's hypotenuse from its two legs, or from one leg and an angle.
Change the values and press Calculate to work out your own figures.
From both legs
Enter the two legs.
Show the working
- c = √(a² + b²)
- c = 5
From a leg and the angle next to it
Enter leg a and angle β (next to leg a).
Show the working
- c = a ÷ cos β (β is the angle next to leg a)
- c = 4.618802154
From a leg and the angle opposite it
Enter leg a and angle α (opposite leg a).
Show the working
- c = a ÷ sin α (α is the angle opposite leg a)
- c = 6
How to use it
Enter the two legs. Enter leg a and angle β (next to leg a). Enter leg a and angle α (opposite leg a).
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
c = √(a² + b²) = a ÷ cos β = a ÷ sin α
Which angle?
The adjacent angle is at the end of the leg; the opposite angle faces it.
Questions
What is the hypotenuse with legs 3 and 4?
5.
And with leg 3 opposite 30°?
6.
Formulas
c = √(a² + b²) = a ÷ cos β = a ÷ sin α
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).