When to use this calculator
Use inverse tangent for a rise-to-run ratio. For direction around a full circle, an atan2 calculation is needed instead.
Explore the trigonometry calculators for other questions in this topic. For a related calculation, use the Cosecant Calculator: Find the reciprocal sine of an angle entered in degrees.
PUTTING IT INTO PRACTICE
Arctangent: 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 |
|---|---|
| Tangent ratio | 1 |
| Result | 45 degrees |
- Check the input labels and enter the example values above.
- Apply the relationship: Angle = atan(ratio) × 180/π.
- The result is 45 degrees, rounded for display.
How to interpret your result
Returns an angle between −90° and 90° and does not resolve the quadrant from two coordinates.
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 arctangent calculator useful?
Use inverse tangent for a rise-to-run ratio. For direction around a full circle, an atan2 calculation is needed instead.
How do I use the arctangent calculator?
Enter tangent 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 = atan(ratio) × 180/π.
What should I check before using the result?
Returns an angle between −90° and 90° and does not resolve the quadrant from two coordinates.
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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