Math
Law of Cosines Calculator
Use the law of cosines calculator when a triangle is not necessarily right and you know two sides with the included angle.
Try an example
Result
Side c
—
- Triangle area
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the law of cosines calculator solves
Use the law of cosines calculator when a triangle is not necessarily right and you know two sides with the included angle.
Formula
How to use it
- Enter two side lengths.
- Enter the included angle between them.
- Read the third side and area.
How to read the answer
When the included angle is 90 degrees, the law of cosines becomes the Pythagorean theorem.
Common mistakes and edge cases
- Use the included angle between the two known sides.
- Keep calculator angle mode in degrees if checking manually.
- Angles must be between 0 and 180 degrees.
Worked examples
Included angle 60 degrees
Side c
8.1854
Obtuse triangle
Side c
11.3578
Frequently asked questions
When should I use law of cosines?+
Use it for SAS triangles or when you know all three sides and need an angle.
Can this handle right triangles?+
Yes, but the Pythagorean theorem is simpler when the angle is exactly 90 degrees.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 15, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 15, 2026