Law of Cosines Calculator

Use our free law of cosines calculator to solve any triangle. Supports SSS (three sides) and SAS (two sides + included angle).

Math

Input Mode

Side a

Side b

Side c

Angle C (included)

Formula

The law of cosines relates the sides of a triangle to the cosine of one of its angles. Use SSS to find angles or SAS to find the third side.

c² = a² + b² - 2ab·cos(C)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select SSS (three sides) or SAS (two sides + included angle).
2Enter the known values.
3Click Calculate.

Examples

SSS: a=5, b=6, c=7

1.cos(C)=(25+36-49)/(2×5×6)=12/60=0.2
2.C≈78.46°, B≈57.12°, A≈44.42°

Result: 7.0000

SAS: a=5, b=7, C=60°

1.c²=25+49-2×5×7×0.5=74-35=39
2.c≈6.245

Result: 6.2450

Frequently Asked Questions

c² = a² + b² - 2ab·cos(C). Generalizes Pythagorean theorem.

Three sides known, computes all three angles.

Two sides and the included angle, computes the third side.

When C=90°, cos(C)=0, so c²=a²+b².

Law of cosines for SSS or SAS; law of sines for AAS, ASA, or SSA.

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CalculateMe Team

Last updated: 2026-07-14

Law of Cosines Calculator

Formula

How It Works

Examples

SSS: a=5, b=6, c=7

SAS: a=5, b=7, C=60°

Frequently Asked Questions

What is the law of cosines?

What is SSS?

What is SAS?

Relation to Pythagoras?

When to use law of sines vs cosines?

Related Calculators

Law of Cosines Calculator

Formula

How It Works

Examples

SSS: a=5, b=6, c=7

SAS: a=5, b=7, C=60°

Frequently Asked Questions

What is the law of cosines?

What is SSS?

What is SAS?

Relation to Pythagoras?

When to use law of sines vs cosines?

Related Calculators