CalcaTools

Inverse Sin Calculator | Find Arcsine in Degrees or Radians

Convert a sine ratio to its angle with arcsin, in degrees or radians, including the second solution in the full circle. Shows the principal range — ideal for trigonometry, physics and engineering problems.

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.

school Free for classroom use

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.

tips_and_updates Pair with the spoke articles

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

lightbulb Worked example

Let's say you are using the Inverse Sine Calculator | Arcsin Angle Tool. Finds the inverse sine (arcsine) of any value between −1 and 1. Enter a number and choose degrees or radians, and the tool returns the angle whose sine equals that value, along with the Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula θ = arcsin(x), −90° ≤ θ ≤ 90°; second solution in [0°, 360°): 180° − θ and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

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

The Inverse Sine Calculator | Arcsin Angle Tool is built on a well-established calculation method. It uses the formula θ = arcsin(x), −90° ≤ θ ≤ 90°; second solution in [0°, 360°): 180° − θ to turn your inputs into a reliable result. Finds the inverse sine (arcsine) of any value between −1 and 1. Enter a number and choose degrees or radians, and the tool returns the angle whose sine equals that value, along with the principal-angle working. Useful The steps are shown on the page so you can follow the reasoning from input to output.

  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°.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is arcsin of 0.5?
The Inverse Sine Calculator | Arcsin Angle Tool is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Finds the inverse sine (arcsine) of any value between −1 and 1. Enter a number and choose degrees or radians, and the tool returns the angle whose sine equals that value, along with the principal-angle working. Useful for trigonometry homework, physics There is no limit on usage, and it works on any device.
How do I do inverse sine on a calculator?
Enter the required values into the input fields and press the calculate button. The tool applies the formula θ = arcsin(x), −90° ≤ θ ≤ 90°; second solution in [0°, 360°): 180° − θ and returns the result with a short explanation of each step, so you can check the working yourself.
Why is arcsin undefined for values over 1?
Because the sine of any real angle is always between −1 and 1 — there is no real angle whose sine exceeds 1. The domain of arcsin is therefore restricted to [−1, 1], and inputs outside that range have no real solution. The calculator flags these inputs rather than returning an error, and for complex analysis the results exist but are outside real trigonometry.
What range does arcsin return?
The Inverse Sine Calculator | Arcsin Angle Tool is a free online tool that finds the inverse sine (arcsine) of any value between −1 and 1. enter a number and choose degrees or radians, and the tool returns the angle whose sine equals that value, along with the principal-angle working. useful for trigonometry homework, physics. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
What's the difference between arcsin and cosecant?
They are completely different functions with confusingly similar names. Arcsin (sin⁻¹) answers 'what angle has this sine?' — arcsin(0.5) = 30°. Cosecant (csc) is the reciprocal of the sine VALUE: csc(30°) = 1 ÷ 0.5 = 2. The superscript −1 in sin⁻¹ means inverse function, not reciprocal. The calculator applies arcsin, the inverse function.
What does the Inverse Sine Calculator | Arcsin Angle Tool do?
Finds the inverse sine (arcsine) of any value between −1 and 1. Enter a number and choose degrees or radians, and the tool returns the angle whose sine equals that value, along with the principal-angle working. Useful for trigonometry homework, physics. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Inverse Sine Calculator | Arcsin Angle Tool use?
It computes θ = arcsin(x) for inputs between −1 and 1, returning the principal angle in the range −90° to 90°, and also shows the second solution 180° − θ for angles within a full 0°–360° circle. For example, arcsin(0.5) = 30°, with a supplementary solution at 150°. Choose degrees or radians as needed.
Is the Inverse Sine Calculator | Arcsin Angle Tool free and private?
Yes — the Inverse Sine Calculator | Arcsin Angle Tool. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Inverse Sine Calculator | Arcsin Angle Tool?
The Inverse Sine Calculator | Arcsin Angle Tool applies the standard formula: θ = arcsin(x), −90° ≤ θ ≤ 90°; second solution in [0°, 360°): 180° − θ. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

Explore the full math toolkit

Every CalcaTools math calculator — algebra, geometry, trigonometry, statistics, sequences, and unit conversions — with step-by-step workings on every result.