Right Triangle Inradius and Circumradius Calculator

Calculate Inradius and Circumradius

This page calculates inradius and circumradius values for right triangles. It is useful for circle-based geometry tasks and clearance or fit calculations.

Circle Relations in Right Triangles

Inradius is solved from side relations (r = (a + b - c)/2), while circumradius follows directly from the right-triangle rule R = c/2.

Which Mode To Pick: Inradius comes from the sides (r = (a + b - c) / 2) and circumradius is always half the hypotenuse (R = c / 2). If you need both, solve the sides first, then each radius follows directly. The strict mode rejects impossible triangles.

Where This Calculator Helps

• Designing inscribed or circumscribed circular features around triangular parts.
• Checking geometry solutions involving triangle-circle relationships.
• Deriving radius values needed for advanced area and construction formulas.

Input Tips for Better Results

• Ensure the triangle is valid and the hypotenuse is the longest side.
• Circumradius depends only on hypotenuse, so c accuracy is critical.
• Inradius should always return a positive value for a valid right triangle.

Pro Tip: If radius values look unusual, re-check side validity with the side calculator first.

How To Use This Calculator

1. Choose the tab that matches your known values before entering numbers.
2. Enter values in consistent units and verify that your triangle inputs are valid.
3. Review the calculated result, then cross-check with a related calculator when accuracy matters.
4. Use related pages such as Right Triangle Perimeter and Semiperimeter Calculator and Right Triangle Area Calculator for advanced checks.

Calculator Modes Available

• Inradius: Radius of the inscribed circle in a right triangle.
• Circumradius: Radius of the circumscribed circle in a right triangle.

Common Mistakes and Quick Fixes

• Mixing units in a single calculation. Keep all values in one unit system before solving.
• Choosing a mode that does not match known inputs. Start with the closest mode to your available values.
• Rounding too early. Keep full precision until the final result output.
• Skipping verification. Recheck using one related calculator before using results in high-stakes work.