What Is a Tangent Calculator?
A tangent calculator finds the tangent of an angle — tan(θ) — or works backward to find the angle from a tangent value using the inverse tangent (arctan). Tangent is one of the three primary trigonometric functions and appears throughout geometry, physics, navigation, and engineering. Enter an angle in degrees or radians to get its tangent, or enter a ratio to get the arctangent.
How to Use the Calculator
- Choose the operation — tangent or inverse tangent (arctan).
- Enter the angle (in degrees or radians) or the value.
- Calculate — see the result.
What Tangent Means
In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side:
tan(θ) = Opposite ÷ Adjacent
On the unit circle, tangent equals sine divided by cosine: tan(θ) = sin(θ) ÷ cos(θ).
Common Tangent Values
| Angle | tan(θ) |
|---|---|
| 0° | 0 |
| 30° | 0.577 |
| 45° | 1 |
| 60° | 1.732 |
| 90° | undefined |
Inverse Tangent (Arctan)
The inverse tangent, written tan⁻¹ or arctan, finds the angle whose tangent is a given value. For example, arctan(1) = 45°. It is essential for finding angles from side ratios in right triangles and for converting coordinates.
Where Tangent Is Used
- Right triangles: finding sides and angles.
- Slopes and grades: the tangent of the incline angle equals rise over run.
- Navigation and surveying: bearings and heights.
- Physics: resolving vectors and angles.
Frequently Asked Questions
What is the tangent of an angle?
In a right triangle, tangent is the ratio of the opposite side to the adjacent side. On the unit circle it equals sine divided by cosine.
Why is tan(90°) undefined?
Because cosine of 90° is zero, and tangent is sine over cosine, dividing by zero makes tan(90°) undefined.
What is the inverse tangent?
The inverse tangent, or arctan, finds the angle whose tangent equals a given value. For instance, arctan(1) equals 45°.
How is tangent related to slope?
The slope of a line equals the tangent of its angle of inclination — tan(angle) = rise ÷ run, so a 45° slope has a tangent of 1.
Is this tangent calculator free?
Yes — it is completely free, requires no signup, and handles both tangent and arctangent.