When to use this calculator
Inverse cosine can recover an angle from an adjacent-to-hypotenuse ratio or a cosine-law calculation.
Explore the trigonometry calculators for other questions in this topic. For a related calculation, use the Arcsine Calculator: Find the principal angle whose sine equals a chosen ratio.
PUTTING IT INTO PRACTICE
Arccosine: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Cosine ratio | 0.5 |
| Result | 60 degrees |
- Check the input labels and enter the example values above.
- Apply the relationship: Angle = acos(ratio) × 180/π.
- The result is 60 degrees, rounded for display.
How to interpret your result
The ratio must lie between −1 and 1. The output ranges from 0° to 180°.
These tools take degrees unless stated otherwise. A right-triangle ratio and the law of cosines solve different input patterns. For the sine rule, identify which side is opposite each supplied angle.
Frequently asked questions
Are the angle inputs in degrees or radians?
The trigonometry tools here label angles in degrees and convert internally. Use the degree-to-radian converter when another formula requires radians.
When is the arccosine calculator useful?
Inverse cosine can recover an angle from an adjacent-to-hypotenuse ratio or a cosine-law calculation.
How do I use the arccosine calculator?
Enter cosine ratio. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Angle = acos(ratio) × 180/π.
What should I check before using the result?
The ratio must lie between −1 and 1. The output ranges from 0° to 180°.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: basic functions and identities ↗. This is a topic reference, not an external review or endorsement of this tool.
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