Right Triangle CalculatorFree online math calculator — instant results, no sign-up
Solve a right triangle from its two legs.
About the Right Triangle Calculator
This calculator computes the hypotenuse, enclosed area, and both acute angles of a right triangle given the lengths of its two perpendicular legs. It is commonly used by students, carpenters, engineers, and surveyors needing rapid geometric solutions.
- Leg a
- Length of the first perpendicular leg, expressed in any consistent linear unit (must be greater than 0).
- Leg b
- Length of the second perpendicular leg, adjacent to angle α and opposite angle β, in the same units as leg a (must be greater than 0).
Formula and method
Hypotenuse = √(a² + b²) Area = (a × b) / 2 Angle α = arctan(a / b) × (180 / π) Angle β = arctan(b / a) × (180 / π)
- aLength of leg a (opposite to angle α)
- bLength of leg b (opposite to angle β)
- αAcute angle opposite leg a, in degrees
- βAcute angle opposite leg b, in degrees
The calculator evaluates the hypotenuse using the Pythagorean theorem via the hypotenuse function. The area is computed as half the base times height, and the two acute angles are calculated using the inverse tangent function converted from radians to degrees, rounded to four decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Leg a3
- Leg b4
Results
- Hypotenuse5
- Area6
- Angle α36.8699°
- Angle β53.1301°
How to use the Right Triangle Calculator
- 1Enter the positive numerical lengths for leg a and leg b.
- 2Compute the hypotenuse using the square root of the sum of squares: √(a² + b²).
- 3Calculate the triangle area by multiplying leg a and leg b, then dividing by 2.
- 4Derive angle α via arctan(a / b) and angle β via arctan(b / a), converting both from radians to degrees.
Reading your result
The hypotenuse and area share the distance and squared units of your input lengths, respectively. Angle α and Angle β are complementary acute angles that sum to exactly 90°, representing the interior angles opposite each respective leg.
Limitations
This calculator strictly solves planar right triangles with a fixed 90° angle between leg a and leg b. It does not accept the hypotenuse or an angle as an input, nor does it handle non-Euclidean spherical or hyperbolic geometry.
Common questions
Which angle corresponds to which leg?+
Angle α is opposite to leg a (adjacent to leg b), while Angle β is opposite to leg b (adjacent to leg a).
Do Angle α and Angle β always sum to 90 degrees?+
Yes. Because the interior angles of a planar triangle sum to 180° and the right angle accounts for 90°, the remaining two acute angles always sum to 90°.
Can I use different units of measurement for leg a and leg b?+
No. Both leg lengths must be in the same unit (such as inches, meters, or feet) before entering them into the calculator to get accurate area and hypotenuse values.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.