Tangent Calculator
Slope, Expressed as an Angle
Tangent is the ratio of the opposite side to the adjacent side in a right triangle, and equivalently the ratio of sine to cosine at any angle. It has a direct geometric meaning too: tan(θ) is literally the slope of a line making angle θ with the horizontal, which is why it shows up constantly in grade calculations, roof pitches, and line-of-sight problems.
The Formula
Because tangent is a ratio involving cosine in the denominator, it's undefined wherever cosine equals zero — at 90° and 270°, and every 180° from those points. The calculator detects this near-zero denominator and returns an explicit error rather than an unreliable extreme value.
Where Tangent Is Used
- Slope and grade — road grades, roof pitches, and ramp angles are all tangent relationships.
- Surveying — finding the height of an object from a measured angle and known horizontal distance.
- Physics — projectile launch angles and friction coefficients both involve tangent.
- Computer graphics — camera field-of-view calculations use tangent to relate angle to screen distance.
| Angle | tan(θ) |
|---|---|
| 0° | 0 |
| 30° | 0.57735 |
| 45° | 1 |
| 60° | 1.732051 |
| 90° | undefined |
How to Use This Calculator
- Enter the Angle.
- Select the unit: Degrees or Radians.
- Select Calculate to see the tangent value.
Related Calculations
Need the reciprocal ratio? The Cotangent Calculator computes 1/tan(θ). To solve for the angle given a tangent value, use the Trigonometric Equation Solver.