Right Triangle Calculator With Altitude
Enter the two legs of a right triangle, side a and side b, and press Calculate. Each leg takes a length from 0.000000001 to 1,000,000,000,000, and both must use the same unit. The calculator returns the hypotenuse c, the acute angles α and β in degrees, the area, the perimeter, the altitude to the hypotenuse and the two segments it cuts c into. It starts from the two legs only. If you know an angle or the hypotenuse instead, the FAQ below shows how to get the legs first.
How to use the Right Triangle Calculator
- Enter your numbers in the Right Triangle Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The right triangle relationships
c = √(a² + b²) · · · α = arctan(a / b) · · · β = arctan(b / a) = 90° − α · · · Area = ½ · a · b · · · Perimeter = a + b + c · · · Altitude h = a · b / c · · · p = a² / c · · · q = b² / c
a and b are the legs and c is the hypotenuse, opposite the right angle. α is the angle opposite side a and β the angle opposite side b. The calculator finds c with the Pythagorean theorem and each angle with its own arctangent. The two angles always add up to 90°. The altitude h runs from the right angle to side c and meets it at a right angle. Its foot cuts c into a segment p next to leg a and a segment q next to leg b, with p + q = c and h² = p × q.
Worked example
Legs a = 6 and b = 8: c = √(36 + 64) = 10. α = arctan(6 / 8) = 36.87° and β = 90° − 36.87° = 53.13°. Area = ½ × 6 × 8 = 24. Perimeter = 6 + 8 + 10 = 24. Altitude h = 6 × 8 / 10 = 4.8. The segments are p = 36 / 10 = 3.6 and q = 64 / 10 = 6.4, which add up to c, and 3.6 × 6.4 = 23.04 = 4.8².
Frequently asked questions
How do I find the altitude of a right triangle?
Multiply the two legs and divide by the hypotenuse: h = (a × b) / c. For legs 6 and 8 that is 48 / 10 = 4.8, and the calculator shows it as Altitude h to c. The altitude splits the triangle into two smaller right triangles similar to the original. It comes from the area, because ½ × a × b and ½ × c × h are the same triangle.
How do I solve from one angle and one side?
Work out the two legs first, then enter them. With angle α and the hypotenuse c, a = c × sin(α) and b = c × cos(α). With α and leg b, a = b × tan(α).
What if I know one leg and the hypotenuse?
Find the other leg with b = √(c² − a²), or use the Pythagorean Theorem Calculator, which solves for a missing leg. Then enter both legs here to get the angles, area and perimeter.
Why does an angle say below 0.01?
A right triangle cannot have a second angle of 0° or 90°, but a very thin one rounds to those at two decimals. Legs 1 and 1,000,000 give α below 0.01 and β above 89.99, with a note to check that both legs use the same unit.