Law of Cosines Calculator

Formula

c=√(a²+b²−2ab cos C)

Worked example

a=3,b=4,C=90° — 5

Quick answer

What does the Law of Cosines Calculator do?

Find side c from sides a, b and included angle C.

What is the Law of Cosines Calculator?

Find side c from sides a, b and included angle C. Use it when you have the required inputs and want a deterministic, repeatable result with the calculation method visible.

How to use this calculator

Enter the values requested by the tool, keep units and time periods consistent, resolve any validation message, calculate, then review the primary answer together with the displayed formula and supporting values.

Formula and method

This calculator uses the deterministic formula c=√(a²+b²−2ab cos C). Enter the required values, then review the displayed substitution and result breakdown to verify the calculation.

Worked example

a=3,b=4,C=90° 5

Common mistakes to avoid

Check units, decimal points, percentages, signs, date/time order, selector choices, and rounding. For important decisions, verify the result against an independent source or qualified professional when appropriate.