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Trigonometry Calculator

Find sine, cosine, tangent, cosecant, secant and cotangent of any angle, in degrees, radians or gradians.

Written by Jude Ramsey · Last updated August 2026 · How these calculators are checked

How the trigonometry calculator works

All six trigonometric functions come from the same two: cosecant, secant and cotangent are simply the reciprocals of sine, cosine and tangent. The calculator computes all of them and flags the ones that are undefined at your angle.

The inverse mode goes the other way: give it a ratio and it returns the angle. That is the operation you need when solving triangles from side lengths rather than angles.

Step by step

  1. Enter the angle and choose degrees, radians or gradians.
  2. Read all six function values.
  3. Switch to inverse mode to find an angle from a ratio.

The maths behind it

tan = sin ÷ cos · csc = 1 ÷ sin · sec = 1 ÷ cos · cot = cos ÷ sin degrees × π/180 = radians

Worked example

As an example, with a or find the angle from a ratio of Not using inverse, ratio value for the inverse of 0.5, the calculator returns a sin of 0.5. Underneath, cos comes out at 0.866025 and tan at 0.57735. Change any field and every figure updates as you type.

FAQ

Why is tangent undefined at 90 degrees?
Because cosine is zero there, and tangent is sine divided by cosine. The same happens at every odd multiple of 90 degrees.
What are gradians?
A unit where a right angle is 100 units instead of 90. Some surveying and engineering work still uses them.
What range do inverse functions return?
Arcsine and arctangent return −90° to 90°; arccosine returns 0° to 180°. Those are the standard principal values.

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