Arcsine Calculator

sin⁻¹(x) — find the angle whose sine is x. Domain [-1, 1], range [−90°, 90°].

Inputs

Result

Loading calculator…
—

General calculation reads

Amazon affiliate
How Not to Be Wrong
Jordan Ellenberg - math thinking
Shop on Amazon
The Joy of X
Steven Strogatz - accessible math
Shop on Amazon
Scientific calculator (Casio fx-991EX)
Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

  • Enter a value between -1 and 1.
  • Read the angle in your chosen unit.

About this calculator

arcsin (sin⁻¹) returns the angle whose sine is the input. Domain is [−1, 1]; outside this range there is no real solution. Principal range is [−90°, 90°] (or [−π/2, π/2] in radians).

Frequently asked

Why is the range only -90° to 90°?+
Sine isn't one-to-one over its full domain — sin(30°) = sin(150°). The "principal" arcsin returns the value in [−90°, 90°] for uniqueness.
What if my input is outside [-1, 1]?+
No real solution; the calculator shows "—". sin only returns values in [−1, 1].
Common values to remember?+
arcsin(0) = 0°, arcsin(½) = 30°, arcsin(√2/2) = 45°, arcsin(√3/2) = 60°, arcsin(1) = 90°.
Is arcsin the same as 1/sin?+
No — 1/sin is cosecant (csc). arcsin is the inverse function.
Can I get an answer in radians?+
Yes — toggle the output unit to "Radians".

Related calculators

Sine Calculator
Compute sin(x) for any angle in degrees or radians.
Arccosine Calculator
cos⁻¹(x) — find the angle whose cosine is x. Range [0°, 180°].
Arctangent Calculator
tan⁻¹(x) — find the angle whose tangent is x. Range (−90°, 90°).
Cosine Calculator
Compute cos(x) for any angle.
Tangent Calculator
tan(x) = sin(x) / cos(x). Undefined where cos(x) = 0 (at 90°, 270°, …).
Unit Circle Calculator
Angle θ → (cos θ, sin θ) coordinates on the unit circle. Reference angle + quadrant.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

Arccosine Calculator
Calc

cos⁻¹(x) — find the angle whose cosine is x. Range [0°, 180°].

Arctangent Calculator
Calc

tan⁻¹(x) — find the angle whose tangent is x. Range (−90°, 90°).

Sine Calculator
Calc

Compute sin(x) for any angle in degrees or radians.

Unit Circle Calculator
Calc

Angle θ → (cos θ, sin θ) coordinates on the unit circle. Reference angle + quadrant.

Cosine Calculator
Calc

Compute cos(x) for any angle.

Ideal Weight Calculator
Health

Healthy-weight range from WHO BMI categories + Devine, Robinson, Miller, and Hamwi formulas (heights ≥152 cm / 5 ft).