Cosine Rule Calculator
📐 Trigonometry & Pythagoras. Use the Cosine rule formula to find side a, side b, side c, angle a (between b and c): pick the value you want, type the others, and the answer updates as you go.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Side a | cm |
| Side b | cm |
| Side c | cm |
| Angle A (between b and c) | ° |
Worked example
Find the side a when Side b = 5 cm, Side c = 7 cm, Angle A (between b and c) = 58.4 °.
Using a² = b² + c² - 2bccos A: Side a = 6.1091 cm.
Frequently asked questions
What is the formula for Cosine rule?
a² = b² + c² - 2bccos A.
What do the letters stand for, and what units are used?
Side a in cm, Side b in cm, Side c in cm, Angle A (between b and c) in °.
How do you calculate side a?
Put the values into a² = b² + c² - 2bccos A. For example, with Side b = 5 cm, Side c = 7 cm, Angle A (between b and c) = 58.4 °, side a = 6.1091 cm.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (side a, side b, side c, angle a (between b and c)) and fill in the others: it rearranges the formula for you.
