Arccosine Calculator

How it is calculated

You enter a cosine value v, a unitless ratio. The tool returns θ = arccos(v), the single angle between 0° and 180° whose cosine equals v. It is computed in radians and shown to 6 decimal places, then converted with θdeg = θrad × 180 ÷ π and shown to 4 decimal places. Cosine never leaves the range −1 to 1, so a value such as 1.01 or −3, and an empty box, give no result. The ends behave as expected: v = 1 gives 0°, v = 0 gives 90° and v = −1 gives 180°. A positive v always gives an acute angle and a negative v an obtuse one. Unlike arcsine, the result is never negative.

Common mistakes

• Entering the angle where the cosine value belongs. The box wants a ratio from −1 to 1, not 60.
• Dropping the minus sign. arccos(0.5) is 60° but arccos(−0.5) is 120°; the sign decides whether the angle is acute or obtuse.
• Forgetting to normalize a dot product. For vectors you must divide by both lengths first; the raw dot product is usually larger than 1 and will be refused.
• Expecting a negative angle like arcsine gives. The output here always runs from 0° to 180°.
• Reading the radians line as degrees. 1.047198 is 60° expressed in radians, not about one degree.