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Right Triangle Calculator

Use this Right Triangle Calculator to solve sides, angles, area, and perimeter. Provide exactly two known values (at least one side), then click Calculate.

Conventions: legs are a and b, hypotenuse is c. Angles A and B are the acute angles opposite sides a and b respectively (C = 90°).

Fill only the fields required by your chosen method. Angles must be in degrees between 0 and 90 (exclusive).

Results are rounded to the selected number of decimal places.

Tip: If you enter both angles, the triangle is underdetermined without a side. Make sure at least one side length is included among your two known values.

Quickly solve any right triangle by entering two known values. Our Right Triangle Calculator uses classic trigonometry and the Pythagorean theorem to find missing sides, angles, area, and perimeter with precision.

How the Right Triangle Calculator Works

A right triangle has one 90° angle and two acute angles that sum to 90°. The sides are named as follows: a and b are the legs that form the right angle, and c is the hypotenuse opposite the right angle. If you provide any two independent values (with at least one side), the remaining measurements are uniquely determined.

  • Given a and b: c = ?(a² + b²), angles from arctangent.
  • Given a and c: b = ?(c² - a²), angles from arcsine.
  • Given b and c: a = ?(c² - b²).
  • Given a and A: use sine, cosine, and tangent to derive c and b.
  • Given b and B: symmetric to the case above.
  • Given c and A (or B): legs from sine and cosine.

The calculator also returns area and perimeter:

  • Area = (a × b) ? 2
  • Perimeter = a + b + c

Step-by-Step: Using the Calculator

  1. Select what you know (for example, “Legs a & b” or “Hypotenuse c & angle A”).
  2. Enter your two known values in the corresponding fields.
  3. Choose the desired number of decimal places.
  4. Click Calculate to get sides, angles, area, and perimeter.

Right Triangle Formulas Explained

The Pythagorean theorem states that for any right triangle, a² + b² = c². Trigonometric ratios connect sides and angles:

  • sin(A) = a ? c, cos(A) = b ? c, tan(A) = a ? b
  • sin(B) = b ? c, cos(B) = a ? c, tan(B) = b ? a
  • A + B = 90°

From these, you can derive any missing dimension when two independent values are known. For instance, if you know a and A, then c = a ? sin(A) and b = a ? tan(A). If you know c and A, then a = c × sin(A) and b = c × cos(A).

Practical Uses

Right triangles appear everywhere: carpentry (squaring corners), surveying distances, navigation bearings, ramp design for accessibility, and calculating roof pitch. This calculator lets you verify measurements, plan cuts, and ensure code compliance by translating between angles and lengths with ease.

Accuracy Tips

  • Use consistent units for all side lengths (meters, feet, etc.).
  • Measure angles in degrees as entered; the tool converts internally for trigonometric functions.
  • When using a side and an angle, ensure the angle is one of the acute angles (strictly between 0° and 90°).
  • If the hypotenuse is less than or equal to either leg, the inputs are invalid.

Example

Suppose a = 3 and b = 4. The calculator computes c = ?(3² + 4²) = 5. Angle A = arctan(3 ? 4) ? 36.87° and B = 53.13°. Area = (3 × 4) ? 2 = 6, and perimeter = 3 + 4 + 5 = 12.

Why Use This Right Triangle Calculator?

  • Fast and accurate solutions with clear formulas.
  • Multiple input combinations supported.
  • Adjustable precision for engineering or classroom needs.

Enter two values now and instantly unlock the rest of your right triangle’s dimensions.

FAQs

How do I use the Right Triangle Calculator with two legs?

Choose “Legs a & b,” enter a and b, and the calculator finds c, both angles, area, and perimeter.

Can the Right Triangle Calculator solve from one leg and one angle?

Yes. Select the matching method (e.g., a & A), enter values in degrees, and it computes all remaining sides and angles.

What units does the Right Triangle Calculator use?

Any length unit works as long as you stay consistent. The outputs use the same unit you entered.

Does the Right Triangle Calculator handle the hypotenuse and an angle?

Yes. Pick “Hypotenuse c & angle A” or “Hypotenuse c & angle B” to compute the legs and other values.

Why does the Right Triangle Calculator say my inputs are invalid?

Common issues: c must be greater than each leg, angles must be between 0° and 90°, and all sides must be positive.

Will the Right Triangle Calculator show area and perimeter?

It returns area = (a×b)/2 and perimeter = a + b + c for every valid calculation.

Are angles in the Right Triangle Calculator in degrees or radians?

Enter angles in degrees. The calculator converts internally for accurate trigonometric calculations.