Right Triangle Calculator
Solve a right triangle from any two of its legs, hypotenuse, acute angles, height, area and perimeter, including both answers when two triangles fit.
Change the values and press Calculate to work out your own figures.
Enter any two values, including at least one length.
Show the working
- From the leg a and leg b
- c² = a² + b²; sin α = a ÷ c, cos α = b ÷ c, tan α = a ÷ b (SOH CAH TOA)
How to use it
Enter any two values, including at least one length.
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
a² + b² = c²; sin α = a ÷ c; area = ab ÷ 2; h = ab ÷ c
Two solutions
Some pairs, such as the height and the area, fit two different right triangles that are mirror images in shape: the legs swap roles.
Questions
How do I find the hypotenuse?
c = √(a² + b²): legs 3 and 4 give 5.
Can I use an angle?
Yes: one acute angle and any length solve the triangle.
Formulas
a² + b² = c²; sin α = a ÷ c; area = ab ÷ 2; h = ab ÷ c
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).