Arcsine Calculator

This arcsine calculator returns the arcsine, the angle whose sine equals the value you enter. The result is given in degrees as the headline and in radians beside it. Arcsine is the inverse of the sine function, so it answers the question, what angle has this sine. The input must be between -1 and 1, because sine never goes outside that range. Values outside it have no real angle. 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

Arcsine is the inverse of sine: if sin(theta) = x then arcsin(x) = theta. The principal value lies between -90 and 90 degrees (-pi/2 and pi/2 radians). The input must be in the range -1 to 1.

Worked example

Arcsine of 0.5 is 30 degrees, because sin 30 = 0.5. Enter 0.5 to confirm.

Frequently asked questions

What does arcsine give me?

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

What is the valid input range?

The input must be between -1 and 1, because sine never goes outside that range. Values outside it have no real angle.

In what range is the angle returned?

Arcsine returns an angle between -90 and 90 degrees.

Who this calculator is for

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

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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