Grouped Calculator
Right Triangle Inradius and Circumradius Calculator
Find triangle radii.
Calculator Mode
Back To Right Triangle CalculatorInradius Calculator
This calculator follows and returns Inradius r.
Enter inputs to calculate Inradius r.
Inradius r
Result-
Solution Steps
Formula:
Circumradius Calculator
This calculator follows and returns Circumradius R.
Enter inputs to calculate Circumradius R.
Circumradius R
Result-
Solution Steps
Formula:
Radius Relation r Calculator
This calculator follows and returns Inradius r.
Enter inputs to calculate Inradius r.
Inradius r
Result-
Solution Steps
Formula:
Radius Relation R Calculator
This calculator follows and returns Circumradius R.
Enter inputs to calculate Circumradius R.
Circumradius R
Result-
Solution Steps
Formula:
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.