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Triangle Exradius Calculator

Calculate all three triangle excircle radii. Provide Side a, Side b, Side c to compute results directly in your browser. Strict triangle inequality; r_a=area/(s-a) and corresponding denominators. Same length unit and stable Heron area. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.

Free to useNo sign-upRuns in your browser
Enter your details

Enter the inputs, then select Calculate.

Allowed range: 1e-09 to 1000000000.0.

Allowed range: 1e-09 to 1000000000.0.

Allowed range: 1e-09 to 1000000000.0.

Your result
Enter your details

Result will appear here

How the Triangle Exradius Calculator Works & Core Formula

The Triangle Exradius Calculator evaluates Side a, Side b, Side c in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.

Calculate all three triangle excircle radii.

Strict triangle inequality; r_a=area/(s-a) and corresponding denominators. Same length unit and stable Heron area. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.

Concept diagram for Triangle Exradius Calculator, showing side a input and the supported output.
Concept diagram; the three operation images are actual browser captures.

Triangle Exradius Calculator Quick Reference & Input Guide

Review the input parameters, allowed value ranges, and worked reference cases for the Triangle Exradius Calculator below before running your calculation.

Parameter / ScenarioDefault / Sample ValueRule or Allowed RangeOutput / Usage Note
Input: Side a3Range: 1e-09 to 1000000000.0Required workspace parameter
Input: Side b4Range: 1e-09 to 1000000000.0Required workspace parameter
Input: Side c5Range: 1e-09 to 1000000000.0Required workspace parameter
Worked Case 1: Baseline run (Side a = 3)Preloaded / test valuesCalculate all three triangle excircle radiiSide a = 3; Side b = 4; Side c = 5. The displayed output is Exradius opposite a: 2 Exradius opposite b: 3 Exradius opposite c: 6.
Worked Case 2: Comparison scenario (equilateral triangle exradius formula)Preloaded / test valuesCalculate all three triangle excircle radiiSide a = 5; Side b = 5; Side c = 6. The displayed output is Exradius opposite a: 4 Exradius opposite b: 4 Exradius opposite c: 6.

Step-by-Step Guide to Using the Triangle Exradius Calculator

Follow these three steps to configure Side a, Side b, Side c, verify unit and boundary rules, and export your Triangle Exradius Calculator output.

Enter side a

Enter side a. Allowed range: 1e-09 to 1000000000.0.

Calculate
Input and settings
Triangle Exradius Calculator: input and settings in the implemented browser tool
Actual local browser view. Open the image to read it at full size.

Complete the other inputs

Set side b, side c. Strict triangle inequality; r_a=area/(s-a) and corresponding denominators.

Calculate
Tool result
Triangle Exradius Calculator: tool result in the implemented browser tool
Actual local browser view. Open the image to read it at full size.

Calculate and read the output

Select Calculate to see the three excircle radii. Copy result copies this text; Download saves it as a TXT file.

Calculate
Review the details
Triangle Exradius Calculator: review the details in the implemented browser tool
Actual local browser view. Open the image to read it at full size.

Practical Worked Examples for Triangle Exradius Calculator

These concrete scenarios illustrate how the Triangle Exradius Calculator processes baseline inputs, comparison checks, and boundary constraints.

Baseline run (Side a = 3)

Side a = 3; Side b = 4; Side c = 5. The displayed output is Exradius opposite a: 2 Exradius opposite b: 3 Exradius opposite c: 6.

Calculate
Abstract input values and a mathematical worksheet.
Start with the values. Concept illustration.

Comparison scenario (equilateral triangle exradius formula)

Side a = 5; Side b = 5; Side c = 6. The displayed output is Exradius opposite a: 4 Exradius opposite b: 4 Exradius opposite c: 6.

Calculate
Two calculation examples shown for comparison.
Compare a second example. Concept illustration.

Boundary & unit check (Triangle Exradius Calculator)

When solving for 'triangle exradius calculator', verify that Side a, Side b, Side c use consistent units and stay within the documented scope: Strict triangle inequality; r_a=area/(s-a) and corresponding denominators. Same length unit and stable Heron area. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.

Calculate
A calculation and supporting explanation represented conceptually.
Explain the calculation. Concept illustration.

How to Read and Verify the Triangle Exradius Calculator Output

The output panel reports the exact result derived from Side a, Side b, Side c alongside any unit or formatting notes.

The result is the three excircle radii. Find each external tangent-circle radius from triangle side lengths.

The radius labels identify the opposite side and require a nondegenerate triangle.

Numerical output shows up to 12 significant digits. Floating-point arithmetic and display rounding can affect the last digits.

Example input
Side a = 3; Side b = 4; Side c = 5
Example output
Exradius opposite a: 2 Exradius opposite b: 3 Exradius opposite c: 6
CalculateCalculate
A mathematical result connected to the values used to calculate it.
Read the result with its inputs. Concept illustration.

Scope Limits, Accuracy Assumptions & Related Everyday Math Tools

Review these boundary constraints and validation rules before relying on the Triangle Exradius Calculator output.

Operational scope: Strict triangle inequality; r_a=area/(s-a) and corresponding denominators. Same length unit and stable Heron area. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.

Need an adjacent calculation in Everyday Math? Use the related tools linked below to chain your workflow without leaving your browser.

CalculateCalculate
Values and units reviewed before relying on a mathematical result.
Check values and units. Concept illustration.

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Frequently Asked Questions About Triangle Exradius Calculator

Answers about using Triangle Exradius Calculator and understanding its results.

What formula or rule does the Triangle Exradius Calculator use?

The Triangle Exradius Calculator applies the rule: Calculate all three triangle excircle radii. Enter Side a, Side b, Side c into the workspace and the tool computes the exact output in your browser.

What input parameters and units are required for Triangle Exradius Calculator?

Yes. Provide Side a, Side b, Side c using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.

What are the accuracy limits and boundary assumptions for Triangle Exradius Calculator?

Strict triangle inequality; r_a=area/(s-a) and corresponding denominators. Same length unit and stable Heron area. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.

Is the Triangle Exradius Calculator free and does it keep my inputs private?

Yes. All calculations for the Triangle Exradius Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.

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