Grouped Calculator
Right Triangle Inradius and Circumradius Calculator
Find triangle radii.
Calculator Mode
Back To Right Triangle CalculatorInradius Calculator
This calculator finds Inradius r using r = (a + b − c) / 2.
Enter inputs to calculate Inradius r.
Inradius r
Result-
Solution Steps
Formula: r = (a + b − c) / 2
Circumradius Calculator
This calculator finds Circumradius R using R = c / 2.
Enter inputs to calculate Circumradius R.
Circumradius R
Result-
Solution Steps
Formula: R = c / 2
Radius Relation r Calculator
This calculator finds Inradius r using r = (a + b − c) / 2.
Enter inputs to calculate Inradius r.
Inradius r
Result-
Solution Steps
Formula: r = (a + b − c) / 2
Radius Relation R Calculator
This calculator finds Circumradius R using R = c / 2.
Enter inputs to calculate Circumradius R.
Circumradius R
Result-
Solution Steps
Formula: R = c / 2
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.
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
- Choose the tab that matches your known values before entering numbers.
- Enter values in consistent units and verify that your triangle inputs are valid.
- Review the calculated result, then cross-check with a related calculator when accuracy matters.
- 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.
- Radius Relation r: Inradius of a right triangle.
- Radius Relation R: Circumradius of 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.
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What radius values does this page provide? expand_more
It provides inradius and circumradius for right triangles, including related radius relations used in geometry and construction contexts.
02 What is the right-triangle circumradius shortcut? expand_more
For any right triangle, circumradius is half the hypotenuse, so R = c/2.
03 How is inradius computed on this page? expand_more
A common right-triangle relation used is r = (a + b - c)/2, derived from side geometry and area relations.
04 Why might my inradius result look too small or negative? expand_more
That usually indicates invalid triangle inputs or a side assignment issue. Verify the triangle with side-solving first.
05 Where are radius values useful in practice? expand_more
Radius values are useful for inscribed or circumscribed design checks, circle-fit constraints, and derived geometry workflows.
Related Calculators
Related Radius Calculators
Use these focused calculators if you want to calculate one specific right triangle radius.