CalcaTools

Inverse Sine Calculator | Arcsin Angle Tool

Arcsin of any value between −1 and 1, in degrees and radians, with the second solution.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

sin valuearcsin (degrees)arcsin (radians)
00°0
0.530°π/6
0.707145°π/4
0.866060°π/3
190°π/2
−0.5−30°−π/6

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

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Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

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Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

Input valuePrincipal angle
0 to 10° to 90° (Quadrant I)
−1 to 0−90° to 0° (Quadrant IV)
Outside [−1, 1]Undefined — sine never exceeds 1

Formula & methodology

Formula: θ = arcsin(x), −90° ≤ θ ≤ 90°; second solution in [0°, 360°): 180° − θ

  1. Enter a sine value between −1 and 1.
  2. The calculator returns the principal angle θ = arcsin(x) in degrees and radians.
  3. Because sine is positive in Quadrants I and II, it also lists the second solution 180° − θ.

Worked example: arcsin(0.5) = 30° (π/6 ≈ 0.5236 rad); the other angle with sine 0.5 is 150°.

Frequently asked questions

What is arcsin of 0.5?
30 degrees (π/6 radians). 150° also has sine 0.5 — arcsin returns the principal angle, in Quadrant I or IV.
How do I do inverse sine on a calculator?
Use the sin⁻¹ key, usually shift/2nd + sin. Make sure the angle mode (DEG or RAD) matches the answer you want.
Why is arcsin undefined for values over 1?
Sine of any real angle lies between −1 and 1, so no angle has a sine of, say, 1.5 — the inverse simply doesn't exist there.
What range does arcsin return?
The principal branch: −90° to +90° (−π/2 to π/2). For angles elsewhere, use identities like 180° − θ.
What's the difference between arcsin and cosecant?
Arcsin inverts the sine function (gives an angle); cosecant is 1/sin (gives a ratio). The −1 in sin⁻¹ means inverse, not reciprocal.