Cosine Calculator (cos and arccos)
Find cos θ for an angle in degrees, radians or multiples of π, or the angle from a cosine value, with exact values, reference angle and quadrant.
This calculator gives the cosine of any angle in degrees, radians or multiples of π, and also works backwards: enter a cosine value to get the angle (arccos). For the standard angles such as 30°, 45° and 60°, and every multiple of 15°, it shows the exact value as well as the decimal, plus the reference angle, quadrant and secant that trigonometry homework usually asks for.
How to use this tool
- Choose whether you want cos θ from an angle, or the angle from a cosine value.
- For cos θ, enter the angle and pick degrees, radians or multiples of π (0.25 means π/4).
- For arccos, enter a value between −1 and 1.
- Read the result, the exact form for special angles, and the table of common values.
Formula
cos θ = adjacent ÷ hypotenuse = x-coordinate of the point at angle θ on the unit circle
Radians = degrees × π / 180. On the unit circle cos θ is the x-coordinate, so it is positive in quadrants I and IV and negative in II and III. arccos returns the principal angle between 0° and 180°; the other solution within one full turn is 360° minus that angle.
Example
Find cos 120°. The angle lies in quadrant II and its reference angle is 180° − 120° = 60°, where cos 60° = 1/2. Cosine is negative in quadrant II, so cos 120° = −1/2 = −0.5. Going backwards, arccos(−0.5) = 120°, and the second solution between 0° and 360° is 240°.
Frequently asked questions
Why does my calculator give a different value?
It is probably set to the other angle mode. cos 60 is 0.5 in degrees but about −0.952413 in radians, because 60 radians is roughly 3,438°. Check the unit here and on your calculator.
What is the cosine of 90 degrees?
Exactly 0. Software that works in radians often prints a tiny number such as 6.1e-17 because π/2 cannot be stored exactly; this calculator recognises standard angles and returns the exact value.
Is sec the same as arccos?
No. sec θ = 1 ÷ cos θ is a ratio. arccos, written cos⁻¹, is the inverse function: it takes a ratio and returns an angle. The ⁻¹ in cos⁻¹ does not mean a reciprocal.
Can a cosine be greater than 1?
Not for a real angle. cos θ always lies between −1 and 1, which is why arccos only accepts values in that range.
Last updated: 2026-10-30