Find unknown angles from cosine values or triangle sides, then review precise steps, reference angles, equivalent solutions, units, formulas, and exports.
Select the method that matches your known information. Use cosine value mode when you already know a cosine ratio. Enter any value from minus one through one. The calculator applies inverse cosine and returns the principal angle. It also shows radians, a reference angle, quadrants, and equivalent solutions.
Choose right triangle mode when adjacent and hypotenuse lengths are known. Both lengths must be positive. The hypotenuse must also be longer than the adjacent side. The calculator first divides adjacent by hypotenuse. It then applies inverse cosine to that ratio.
Choose Law of Cosines mode for a non-right triangle. Enter all three side lengths. Then select which angle you want to find. The tool verifies the triangle inequality before calculating. It rearranges the Law of Cosines for the selected angle.
Cosine describes the horizontal relationship of an angle. On a right triangle, cosine compares the adjacent side with the hypotenuse. On the unit circle, cosine equals the point's horizontal coordinate. Positive cosine values appear in quadrants one and four. Negative values appear in quadrants two and three.
Inverse cosine, written cos-1 or arccos, reverses this process. A calculator normally returns one principal value between zero and 180 degrees. However, cosine can repeat the same value at other angles. This tool therefore includes equivalent solutions inside a selected interval.
Angles can be displayed in degrees or radians. One complete turn equals 360 degrees or 2π radians. The calculator shows both units together. You can also select the number of decimal places for rounded results. Exact familiar angles are recognized when the computed value closely matches common special angles.
Use the export buttons to save your work. CSV files store inputs, answers, and steps in a spreadsheet-friendly format. PDF export creates a compact report containing the same calculation details. These exports are useful for homework, checking work, or keeping calculation records.
| Cosine value | Principal angle | Radians | Notes |
|---|---|---|---|
| 1 | 0° | 0 | Maximum cosine |
| 0.866025 | 30° | π/6 | Special angle |
| 0.707107 | 45° | π/4 | Special angle |
| 0.5 | 60° | π/3 | Special angle |
| 0 | 90° | π/2 | Cosine changes sign |
| -0.5 | 120° | 2π/3 | Negative cosine |
Use inverse cosine. Enter the cosine value, then calculate θ = cos-1(x).
Real-angle cosine values cannot exceed one in magnitude.
Inverse cosine returns an angle whose cosine equals the supplied value.
Yes. Within a full turn, most cosine values correspond to two angles.
Multiply radians by 180 ÷ π.
The Law of Cosines links all three side lengths with each angle.
Arccos returns the principal angle, usually between zero and 180 degrees.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.