Free · Trigonometry calculators 📐

Arccosine Principal Angle & Cosine Ratio

Find the principal angle for a cosine ratio, or solve the ratio from an angle between 0° and 180°, with nine angle units.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

The principal inverse cosine of 0.5 is 60°, or π/3 radians. An input of −1 gives 180° and an input of 1 gives 0°.

Angle = arccos(ratio); ratio = cos(angle), with the principal angle from 0 to π radians

Enter these known values and leave the other values blank.

The real-valued cosine ratio must be between −1 and 1, inclusive.
The principal result is from 0° through 180°. Reverse angle entry is restricted to the same branch, allowing only numerical conversion tolerance at its boundaries.
Arccosine is an inverse function. It does not mean one divided by cosine. Other angles with the same cosine are outside this principal-value result.

Yes. Changing the angle selector preserves the physical angle and changes its displayed unit.

Bookify restricts reverse angle entry to the principal inverse-trigonometric branch, with a 1e-50-radian tolerance for unit-conversion rounding.