Arcsine Calculator

This arcsine calculator works out the inverse sine of a number, the angle whose sine equals the value you enter, which matters whenever you need to work backwards from a ratio to an angle rather than forwards from an angle to a ratio, something that comes up constantly in trigonometry, geometry, physics, surveying and navigation. You enter a single value, and it must sit between -1 and 1 inclusive, because sine itself can never produce a result outside that range, so anything beyond it has no real angle and the calculator will say so rather than force a false answer. Once you enter a valid figure, it returns the angle in degrees as the large headline result, the same angle again in radians alongside it, and your original input value repeated underneath so you can check what was calculated. It returns the principal value, the single standard answer arcsine gives, which always falls between -90 and 90 degrees (-pi/2 and pi/2 radians), even though other angles outside that band can share the same sine. Try the worked example of 0.5, which returns exactly 30 degrees because sin 30 equals 0.5, before entering your own figures. Results are rounded for display, so treat tiny decimal differences as rounding rather than a mistake.

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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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