A right triangle is fixed by any two values that include a side. With both legs, the hypotenuse is √(a² + b²); with a leg and the hypotenuse, the other leg is √(c² − a²); with a leg and its opposite angle, c = a ÷ sin A. Legs 3 and 4 give a hypotenuse of 5, an area of 6 and angles of 36.87° and 53.13°.
Students checking homework, carpenters squaring a frame and anyone working out a ramp or roof pitch run into the same problem: two measurements of a right triangle are known and the rest are not. Pick which pair you have, enter the values, and the calculator returns the hypotenuse, both legs, both acute angles in degrees, the area, the perimeter and the altitude dropped onto the hypotenuse. The working lists each formula with your numbers in it. Lengths carry no unit, so the answers come back in whatever unit you entered, and areas in that unit squared. The tool assumes the triangle has an exact 90° corner; for a general triangle, use a solver based on the law of sines and cosines.
Select both legs, a leg and the hypotenuse, or a leg and the angle opposite it.
Type the lengths in any single unit and the angle in degrees; results update as you type.
Check the hypotenuse, the other sides, the angles, area and perimeter, then open the working to see each formula.
Result Hypotenuse c: 5
Leg a: 3
Leg b: 4
Angle A (°): 36.87
Angle B (°): 53.13
Area: 6
Perimeter: 12
Altitude to hypotenuse: 2.4
The classic 3-4-5 triangle: the hypotenuse is exactly 5 and the smaller acute angle is 36.87°.
Result Hypotenuse c: 13
Leg a: 5
Leg b: 12
Angle A (°): 22.62
Angle B (°): 67.38
Area: 30
Perimeter: 30
Altitude to hypotenuse: 4.6154
The missing leg is √(169 − 25) = 12, giving the 5-12-13 triple with area 30.
Result Hypotenuse c: 2
Leg a: 1
Leg b: 1.7321
Angle A (°): 30
Angle B (°): 60
Area: 0.866
Perimeter: 4.7321
Altitude to hypotenuse: 0.866
A 30-60-90 triangle has sides 1, √3 and 2, so the hypotenuse is twice the short leg.
c² = a² + b²; sin A = a ÷ c; tan A = a ÷ b; B = 90° − A
a, bcA, BThe Pythagorean theorem links the three sides, and the sine and tangent ratios link a side to an angle. Whichever pair is entered, the calculator finds the third side and angle A first, then sets B to 90° minus A. Area is half the product of the legs, and the altitude to the hypotenuse is a × b ÷ c, since both expressions equal twice the area divided by a base.
It is the side opposite the right angle and always the longest of the three. If the value you enter as the hypotenuse is not longer than the leg, no right triangle exists and the calculator flags the field.
The two acute angles of a right triangle always add up to 90°, so knowing one gives the other. Together with one side, a single acute angle fixes the whole triangle.
The same unit as your inputs. Enter centimetres and the sides come back in centimetres, the area in square centimetres. Angles are always in degrees.
It is the perpendicular distance from the right-angle corner to the hypotenuse. It equals a × b ÷ c; for the 3-4-5 triangle that is 12 ÷ 5 = 2.4.
Measure 3 units along one edge and 4 along the other; the diagonal between the marks should be exactly 5. Multiples such as 6-8-10 or 9-12-15 work the same way for larger frames.
Yes. Sets such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25 are Pythagorean triples, where a² + b² equals c² exactly with integers.
Using this tool in an assignment, article or report? Copy a citation, or a link for your website.
Tools Directory Editorial Team. (2026, October 13). Right Triangle Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/triangles-and-trigonometry/right-triangle-calculator/
Tools Directory Editorial Team. “Right Triangle Calculator.” Tools Directory, 13 Oct. 2026, https://tools.milunir.com/math/triangles-and-trigonometry/right-triangle-calculator/. Accessed 26 Oct. 2026.
Tools Directory Editorial Team. “Right Triangle Calculator.” Tools Directory. Last modified October 13, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/triangles-and-trigonometry/right-triangle-calculator/.
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