Trigonometry Calculator
Calculate sin, cos, tan and their inverses in degrees or radians, with all three ratios shown at once and the conversion written out.
How to use it
- Pick the function, then enter the angle or the ratio.
- Switch between degrees and radians with the unit dropdown.
- For the direct functions, all three ratios are shown together.
Examples
| sin(30°) | 0.5 |
| cos(60°) | 0.5 |
| arctan(1) | 45° |
Trigonometry relates the angles of a right triangle to the ratios of its sides. Given an angle, sine, cosine and tangent tell you the shape of the triangle; given a ratio, the inverse functions (arcsin, arccos, arctan) tell you the angle. This tool covers all six in one place, in degrees or radians.
The three core ratios
| Function | Definition | Range |
|---|---|---|
| sin θ | opposite ÷ hypotenuse | −1 to 1 |
| cos θ | adjacent ÷ hypotenuse | −1 to 1 |
| tan θ | opposite ÷ adjacent = sin θ ÷ cos θ | unbounded |
Worked example — roof pitch
A roof rises 3 m over a horizontal run of 8 m. The pitch angle is arctan(3 ÷ 8) ≈ 20.6°. Flip the question round — given a 20.6° pitch and an 8 m run — and tan(20.6°) × 8 ≈ 3 m gives the rise back. Builders, surveyors and engineers move between these two directions constantly.
Degrees or radians?
Degrees are the everyday unit for angles — 360° in a full turn. Radians (2π in a full turn) are what calculus and physics use, because derivatives of trig functions only come out clean when the angle is in radians. Switch units with the dropdown; the conversion is radians = degrees × π ÷ 180.
Questions people ask
Why does tan(90°) not have an answer?
Tangent is sine divided by cosine, and cos(90°) is zero. The function has a vertical asymptote there, so floating-point maths returns an enormous number instead.
Degrees or radians — which should I use?
Degrees for geometry and navigation, radians for calculus and physics. Every formula involving derivatives of trig functions assumes radians.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026