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Enter any two known values of a right triangle and instantly get the remaining sides, angles, area, and perimeter.
Example
Given the two legs a = 3 and b = 4:
Hypotenuse c = sqrt(3^2 + 4^2) = 5
Angle A = atan(3/4) = 36.87 deg
Angle B = atan(4/3) = 53.13 deg
Area = (1/2) * 3 * 4 = 6
Perimeter = 3 + 4 + 5 = 12
How it works
Pick which two values you know, type them in, and the tool applies the Pythagorean theorem and basic trigonometry to solve the whole triangle. Angle A is opposite leg a, angle B opposite leg b, and C is the 90 degree right angle.
Good to know
The Right Triangle Calculator solves a complete right triangle from just two known values, so you never have to chain together the Pythagorean theorem and trig functions by hand. It offers three input modes — two legs, a leg and the hypotenuse, or a leg and an acute angle — and from any of those it returns both legs, the hypotenuse, all three angles, the area, and the perimeter. It is handy for students checking homework, DIYers laying out square corners or roof pitches, and anyone who knows a couple of measurements and needs the rest.
Reach for it whenever a problem gives you a right angle plus two facts. Building a ramp where you know the rise and the run? Use the two-legs mode. Have a ladder length (hypotenuse) and its base distance? Use leg + hypotenuse. Know a height and the angle of elevation? Use leg + angle. The big number up top is always the hypotenuse, while the grid below breaks out every side, both acute angles, area, and perimeter at once.
To read the output correctly, keep the labeling straight: leg a and leg b are the two short sides meeting at the right angle, hypotenuse c is the long side opposite it, and the angles are named for the side they face — angle A is across from leg a, angle B across from leg b, and angle C is the fixed 90 degrees. The two acute angles will always add up to 90, which is a quick way to sanity-check a result.
A few practical notes: angles are entered and shown in degrees, not radians, and results are rounded to six decimal places. In leg + hypotenuse mode the hypotenuse must be strictly longer than the leg, and in leg + angle mode the angle you type is treated as angle A (opposite the leg you entered), so the calculator finds b = a/tan(A) and c = a/sin(A). All values must be positive, and the math runs entirely in your browser.
Frequently asked questions
Which side is which, and what does each angle mean?
Leg a and leg b are the two sides that form the right angle; hypotenuse c is the longest side opposite it. Angle A sits opposite leg a, angle B opposite leg b, and angle C is the fixed 90 degree right angle.
In 'Leg + angle' mode, which angle do I enter?
Enter the acute angle A, which is opposite leg a, in degrees (between 0 and 90). The tool finds the other leg with b = a/tan(A), the hypotenuse with c = a/sin(A), and angle B as 90 - A.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
How do you find the hypotenuse of a right triangle from the two legs?
Square each leg, add the two results, and take the square root: c = sqrt(a^2 + b^2). For example, legs of 3 and 4 give sqrt(9 + 16) = sqrt(25) = 5.
How do you find a leg when you know the hypotenuse and the other leg?
Rearrange the Pythagorean theorem to b = sqrt(c^2 - a^2). The hypotenuse must be longer than the known leg, otherwise no valid right triangle exists.
How do you calculate the angles of a right triangle?
One angle is always 90 degrees. For the acute angles, take the inverse tangent of the opposite leg over the adjacent leg, for example angle A = atan(a/b); the third angle is simply 90 minus that value.
What is the 3-4-5 triangle and why is it useful?
It is a right triangle whose sides are in the ratio 3:4:5, a whole-number example of the Pythagorean theorem. Builders use it to mark out a perfect 90-degree corner by measuring 3 and 4 units along two edges and confirming the diagonal is 5.
Do the two non-right angles of a right triangle always add up to 90 degrees?
Yes. Since the three angles of any triangle sum to 180 degrees and one angle is fixed at 90, the two acute angles must add to 90, making them complementary.
What is the difference between the legs and the hypotenuse?
The legs are the two sides that form the right angle, while the hypotenuse is the longest side directly opposite the right angle. The hypotenuse is always greater than either leg.
Can a right triangle have two equal sides?
Yes, an isosceles right triangle has two equal legs and acute angles of 45 degrees each. Its hypotenuse equals a leg multiplied by the square root of 2.
How do you find the area of a right triangle?
Multiply the two legs and divide by two: area = (1/2) x a x b, since the legs serve as the base and height. For legs of 3 and 4, the area is 6.
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