Arcsine Calculator

How it is calculated

You enter a sine value v, a plain ratio with no unit. The tool returns the angle θ = arcsin(v), the one angle between −90° and +90° whose sine equals v. The result is computed in radians first, shown to 6 decimal places, and then converted with θdeg = θrad × 180 ÷ π and shown to 4 decimal places. A sine can never leave the range −1 to 1, so any value outside it, such as 1.2 or −2, gives no result, and so does an empty box. The edges work: v = 1 gives 90°, v = −1 gives −90° and v = 0 gives 0°. Other angles with the same sine, such as 180° − θ, are not shown.

Common mistakes

• Entering an angle instead of a ratio. This box takes the sine value (between −1 and 1), not 30 or 45.
• Typing a percentage such as 80 for 80 %. Enter 0.8; values above 1 are rejected.
• Dividing the wrong sides. Sine is opposite ÷ hypotenuse; using adjacent ÷ hypotenuse gives the cosine, and you would need arccos instead.
• Expecting an obtuse angle. A ratio of 0.5 has two solutions in a full turn, 30° and 150°, but the tool returns only 30°; work out 180° − 30° yourself if the geometry requires it.
• Mixing up the units of the two outputs. The degrees line is 4-decimal degrees, and the radians line is the same angle in radians, so do not combine them.