Cotangent Calculator
Tangent, Flipped
Cotangent is the reciprocal of tangent — equivalently, the ratio of cosine to sine. Where tangent represents slope, cotangent represents its inverse, which makes it the natural choice whenever a problem is set up around the adjacent-over-opposite ratio rather than opposite-over-adjacent.
The Formula
cot(θ) = cos(θ) / sin(θ)
Cotangent is undefined wherever sine equals zero — at 0°, 180°, and every multiple of 180°. The calculator detects this near-zero denominator and returns an explicit error instead.
Where Cotangent Appears
- Calculus — cotangent integrals and derivatives form a standard part of trigonometric calculus.
- Physics — certain wave and resonance equations are expressed more cleanly in terms of cotangent.
- Surveying and construction — run-over-rise slope calculations are a direct cotangent relationship.
| Angle | cot(θ) |
|---|---|
| 30° | 1.732051 |
| 45° | 1 |
| 60° | 0.57735 |
| 90° | 0 |
How to Use This Calculator
- Enter the Angle.
- Select the unit: Degrees or Radians.
- Select Calculate to see the cotangent value.
Related Calculations
Cotangent is the reciprocal of the Tangent Calculator. For the primary sine and cosine ratios, see the Sine Calculator.