Example 1
- x = 0.5
30.000000
What is arcsin(0.5)? School writes 30°. The calculator keeps six zeros.
Arcsin calculator
Type an x from −1 to 1. Arcsin asks for the angle whose sine is x. arcsin(0.5) comes out 30.000000°. arcsin(1) = 90°. arcsin(0) = 0°.
The result is in degrees, not radians. x outside [−1, 1] has no real sine. This implementation then returns 0, not an error message.
Results
Enter data and click Calculate.
How it works
Arcsine undoes sine. You want an angle θ such that sin θ = x. For x = 0.5 school writes 30°. The calculator calls Math.asin and multiplies by 180/π, so 0.5 gives 30.000000, leftover from π in six decimals.
The principal branch of arcsin runs from −90° to 90°. x = 1 gives 90°. x = 0 gives 0°. x = −0.5 gives −30°. A minus in x is an angle below the axis, not an error.
The field is x. It must sit in [−1, 1], because that is where a real sine lives. Typed 2 or −1.2 has no angle. The calculator does not leave a blank: it returns 0. That is the same zero as arcsin(0), so check the range before you trust a zero.
Arccosine takes the same x and returns an angle from 0° to 180°. Arctangent has no wall at ±1. Sine from an angle is on the neighbouring page, the other way.
The header units switch does not multiply anything here. 0.5 stays 30.000000 whatever the label says. This is an angle from a ratio, not a centimetre.
arcsin(0.5) = 30.000000°. arcsin(1) = 90°. arcsin(0) = 0°. arcsin(√2/2) is close to 45°. The inverse sine is in degrees, not radians.
Formula
θ° = Math.asin(x) × 180 / π, when −1 ≤ x ≤ 1; otherwise 0
How to use
- Type x, for example 0.5.
- Click Calculate. arcsin(0.5) comes out 30.000000°.
- 1 gives 90°. 0 gives 0°.
- x outside [−1, 1] also shows 0. That is not arcsin(0), only this branch.
- Sine from an angle lives on the sine card. Here you invert the direction.
arcsin(0.5) = 30.000000°
Arcsin undoes sine. The result is in degrees. arcsin(0.5) = 30.000000°. arcsin(1) = 90°. x outside [−1, 1] returns 0.
- arcsin
- The angle from a sine. 0.5 gives 30.000000°. 1 gives 90°. This is not 1/sin.
- x
- The input from −1 to 1. 0 gives 0°. 2 also shows 0, from another branch.
- degrees
- The result unit. The calculator multiplies asin by 180/π. The output is not radians.
Examples
Example 2
- x = 1
90
What is arcsin(1)? 90°. The largest angle on the principal branch.
Example 3
- x = 0
0
What is arcsin(0)? 0°. Not the same zero as typed 2.
Related calculators
Common questions
What is arcsin(0.5)?
In a notebook, 30°. The result is 30.000000, because 180/π is not clean.
What does arcsine mean?
The angle whose sine is x. Written arcsin(x) or sin⁻¹(x), not 1/sin.
What are arcsin(1) and arcsin(0)?
90° and 0°. The principal branch ends at ±90°.
What if I type 2?
A real sine never reaches 2. The calculator returns 0, not a blank. Check |x| ≤ 1.
Is the result in radians?
No. The calculator multiplies by 180/π and returns degrees.
Does a negative x work?
Yes, when |x| ≤ 1. arcsin(−0.5) = −30°. The minus is the turn.
How is arcsin different from arccos?
Another angle from the same x. arccos(0.5) = 60°, not 30°.
Where is sine of 30°?
On the sine card. Here 0.5 returns to 30.000000°.
Does a comma in 0.5 work?
Yes. 0.5 and 0,5 both give 30.000000.
Why zero on a bad x?
That is how the branch is written: outside [−1, 1] it returns 0. Not a second formula, just this code.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.