Arccosine Calculator

This arccosine calculator returns the arccosine, the angle whose cosine equals the value you enter. The result is given in degrees as the headline and in radians beside it. Arccosine is the inverse of the cosine function, so it answers the question, what angle has this cosine. The input must be between -1 and 1, because cosine never goes outside that range. The calculator computes the principal value, which is the standard single answer in the usual range for this inverse function. Use it for trigonometry and geometry, working back from a ratio to an angle, physics, surveying and navigation. The definition, the domain, a worked example and the assumptions are set out below.

Value (between -1 and 1)

Angle (radians)

Input value

The formula

Arccosine is the inverse of cosine: if cos(theta) = x then arccos(x) = theta. The principal value lies between 0 and 180 degrees (0 and pi radians). The input must be in the range -1 to 1.

Worked example

Arccosine of 0.5 is 60 degrees, because cos 60 = 0.5. Enter 0.5 to confirm.

Frequently asked questions

What does arccosine give me?

The angle whose cosine is the number you enter. It is the inverse of cosine.

What is the valid input range?

The input must be between -1 and 1, because cosine never goes outside that range.

In what range is the angle returned?

Arccosine returns an angle between 0 and 180 degrees.

Who this calculator is for

This calculator is for students, engineers and surveyors who need to find an angle from its cosine.

What this calculator assumes

You enter a value between -1 and 1.
The principal value is returned.
Results are rounded for display.

Formula and sources

Related calculators

Trig Calculator: all six trig functions at once.
Degrees to Radians Calculator: convert angle units.
Right Angle Triangle Calculator: solve a right triangle.

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