What is the Pythagorean theorem?

The Pythagorean theorem states that in any right triangle with legs a and b and hypotenuse c, the sum of the squares of the legs equals the square of the hypotenuse: a² + b² = c².

How do you find the angle of a right triangle?

Use inverse trigonometric functions: α = arcsin(opposite / hypotenuse) or α = arctan(opposite / adjacent). The second acute angle is always 90° - α.

What is the altitude to the hypotenuse?

The altitude h is the perpendicular distance from the 90° right angle vertex to the hypotenuse c. It is calculated as h = (a × b) / c.

Math

↵ to calculate

Right Triangle Calculator — Sides, Angles, Area & Hypotenuse

Free right triangle calculator to calculate sides, angles, area, perimeter, and altitude given any two known values using the Pythagorean theorem and trigonometry.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

📏 Some countries say ‘30 degrees’ and others say ‘86 degrees’ for the same weather! Some say ‘5 km’, others say ‘3 miles’. This tool swaps between them instantly so you always know what it means.

📌 Direct Answer & Summary

The Right Triangle Calculator solves all unknown sides, angles, area, perimeter, and altitude of a 90-degree right triangle from any two known parameters using the Pythagorean theorem and trigonometric functions.

Known Parameters

Leg a

Leg b

Proportionate 90° right triangle diagram

What is Right Triangle Calculator — Sides, Angles, Area & Hypotenuse?

How to use it

1️⃣ Select which two values you know (e.g. Leg a & Leg b, Leg & Hypotenuse, or Leg & Acute Angle).
2️⃣ Enter the numerical values into the input fields.
3️⃣ Instantly view the complete triangle solution: all 3 sides, both acute angles, perimeter, area, and altitude.
4️⃣ Inspect the step-by-step geometric derivations and real-time scaled SVG diagram.

Formula

Pythagorean theorem: a² + b² = c². Area = (a × b) / 2. Altitude h = (a × b) / c. Angles: α + β = 90°, sin(α) = a / c, tan(α) = a / b.

💡 See it in action — a real example

For a triangle with Leg a = 3 and Hypotenuse c = 5: b = √(5² - 3²) = √(25 - 9) = 4. Angle α = arcsin(3/5) ≈ 36.87°, Angle β = 90° - 36.87° = 53.13°. Area = (3 × 4) / 2 = 6, Perimeter = 3 + 4 + 5 = 12.

❓ Common questions

What is the Pythagorean theorem?: The Pythagorean theorem states that in any right triangle with legs a and b and hypotenuse c, the sum of the squares of the legs equals the square of the hypotenuse: a² + b² = c².
How do you find the angle of a right triangle?: Use inverse trigonometric functions: α = arcsin(opposite / hypotenuse) or α = arctan(opposite / adjacent). The second acute angle is always 90° - α.
What is the altitude to the hypotenuse?: The altitude h is the perpendicular distance from the 90° right angle vertex to the hypotenuse c. It is calculated as h = (a × b) / c.