Enter any two known values (at least one must be a side). Leave unknown fields blank, then click Calculate.
What this right triangle calculator does
This tool solves a right triangle quickly and clearly. If you provide enough valid information, it calculates all missing values: legs (a and b), hypotenuse (c), acute angles (A and B), area, and perimeter. It is useful for school math, construction measurements, trigonometry homework, and practical geometry checks.
A right triangle always has one 90° angle. In this calculator, that angle is implied, so angles A and B are the two acute angles. They must add up to 90°.
How to use the calculator
Step-by-step
- Enter any two known values.
- At least one value must be a side length.
- Use positive numbers only.
- Click Calculate.
- Review the solved dimensions and derived measurements.
Input combinations that work well
- Two sides (for example, a and b, or a and c)
- One side + one acute angle (for example, c and A)
- One side + both acute angles (A and B must be complementary)
Core right triangle formulas
The calculator uses standard right triangle relationships:
- Pythagorean theorem: c² = a² + b²
- Sine: sin(A) = a / c
- Cosine: cos(A) = b / c
- Tangent: tan(A) = a / b
- Complementary angles: A + B = 90°
- Area: (a × b) / 2
- Perimeter: a + b + c
Example calculation
Suppose you know a = 6 and b = 8. The calculator computes:
- c = 10 (from the Pythagorean theorem)
- A ≈ 36.87°
- B ≈ 53.13°
- Area = 24
- Perimeter = 24
This is a classic 6-8-10 right triangle, a scaled version of the 3-4-5 triangle.
Common mistakes to avoid
- Entering negative or zero side lengths.
- Entering acute angles outside the (0, 90) range.
- Using inconsistent values (e.g., side and angle that cannot describe the same triangle).
- Forgetting that trigonometric inputs here are in degrees, not radians.
Why this matters in real life
Right triangles show up everywhere: roof pitch calculations, ramp design, navigation, physics vectors, and layout work in woodworking. Having a dependable right triangle solver helps you move from known measurements to unknown distances and angles without manual algebra each time.
Quick FAQ
Can I solve with only angles?
No. Angles alone give shape but not size. You need at least one side length.
What if I enter both A and B?
They should add to 90°. If not, the calculator will show an error.
Does it support decimal values?
Yes. Decimals are fully supported, and results are shown to four decimal places.