Right Triangle Geometry Calculator

Compute missing sides, acute angles, area, and perimeter quickly today. Review steps with precise clarity. Plot triangle dimensions with exports, formulas, and dependable examples.

Calculator Inputs

Fill only the values needed for the selected mode.
Reset

Example Data Table

Case Known Inputs Computed Hypotenuse Area Perimeter Angle A
Classic 3-4-5 a = 3, b = 4 5 6 12 36.87°
Isosceles right triangle a = 5, b = 5 7.0711 12.5 17.0711 45°
Angle and hypotenuse A = 30°, c = 10 10 21.6506 23.6603 30°
Angle and adjacent side A = 40°, b = 7 9.1379 20.5653 22.0125 40°

Formula Used

Pythagorean theorem: c² = a² + b², where c is the hypotenuse.

Angle relations: A + B = 90° because the third angle is 90°.

Basic trigonometry: sin(A) = a / c, cos(A) = b / c, tan(A) = a / b.

Area: Area = (a × b) / 2.

Perimeter: Perimeter = a + b + c.

Altitude to hypotenuse: h = (a × b) / c.

Inradius: r = (a + b - c) / 2.

Circumradius: R = c / 2.

Projections on the hypotenuse: p = a² / c and q = b² / c.

How to Use This Calculator

  1. Choose the solving mode that matches your known measurements.
  2. Enter the required side lengths or acute angle.
  3. Add a unit label such as cm, m, or ft.
  4. Pick the decimal precision for the displayed answers.
  5. Click the calculate button to solve the triangle.
  6. Review sides, angles, area, perimeter, and extra geometric values.
  7. Use the chart to inspect the triangle visually.
  8. Download the results as CSV or PDF when needed.

FAQs

1. What makes a triangle a right triangle?

A right triangle has one angle equal to 90 degrees. The side opposite that angle is the hypotenuse. The remaining two sides are called legs.

2. Which side is the hypotenuse?

The hypotenuse is always the longest side. It sits opposite the right angle. In this calculator, it is labeled c.

3. Can I solve the triangle using only one angle?

One acute angle alone is not enough. You also need at least one side length. This calculator supports angle-plus-side combinations for quick solving.

4. Why must the acute angle stay below 90 degrees?

A right triangle already uses one 90 degree angle. The other two angles must share the remaining 90 degrees, so each must be less than 90 degrees.

5. What is the altitude to the hypotenuse?

It is the perpendicular segment drawn from the right angle to the hypotenuse. This value helps with area and projection relationships.

6. What do projection values mean?

They show how each leg projects onto the hypotenuse. These segments are useful in geometric proofs, similarity work, and engineering layouts.

7. Are the exported files based on the displayed result?

Yes. The CSV and PDF buttons use the current solved result shown above the form. Recalculate first if you change any input values.

8. Can I use any measurement unit?

Yes. Enter any unit label you prefer, such as mm, cm, m, in, or ft. The calculator keeps that label throughout the results.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.