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Cosine Rule Calculator

Enter your values below to get the result first, then scroll for the full explanation and guidance.

Step 1 • Add values

Use the calculator

Enter your values below to generate an instant result. You can update the inputs at any time to compare different scenarios.

Example verified by the calculator's triangle trigonometry reference cases.

Results refresh instantly as values change.

Opposite side c

6.2449979984Two sides and included angle

Opposite side c: 6.2449979984 (Two sides and included angle)

The cosine rule calculates the third side from two sides and their included angle.

Triangle result

The cosine rule calculates the third side from two sides and their included angle.

Result snapshot

A quick visual read of the values behind this result.

Side a5
Side b7
Included angle C60°

Recommended next checks

  • →Keep both side lengths in the same unit.
Side a
5
Side b
7
Included angle C
60°

Try different values to compare results.

Find a triangle's third side from two sides and their included angle using the cosine rule.

Fast to use

Built for comparison

Clear result output

Table of Contents

6

About Cosine Rule Calculator

Cosine Rule Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.

Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.

Calculation method

c = sqrt(a^2 + b^2 - 2ab cos(C)).

Formula explained

Calculation flow

This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.

Formula

Input values -> calculation engine -> instant result

How the result is built

1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.

Example

Example verified by the calculator's triangle trigonometry reference cases.

Assumptions

  • Two positive side lengths in one unit and their included angle strictly between 0 and 180 degrees.

Source basis

  • UK-focused calculator flow
  • Structured input validation
  • Instant result breakdowns

FAQ

Common questions

Two positive side lengths in one unit and their included angle strictly between 0 and 180 degrees.

Trust and notes

Assumptions and important notes

This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.

Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.

  • Two positive side lengths in one unit and their included angle strictly between 0 and 180 degrees.

Method

UK calculator guidance

Last reviewed

April 17, 2026