Sine Calculator

Calculate sine values with detailed step-by-step solutions for angles in degrees or radians, including special angle recognition.

Enter Angle

Angle Value

Angle Unit

Degrees (°)Radians (rad)

• Common angles: 0°, 30°, 45°, 60°, 90°

• π rad = 180°, π/2 rad = 90°

Result

Enter an angle to calculate its sine value

Unit Circle & Sine

On the unit circle, sine represents the y-coordinate of the point where the angle intersects the circle.

sin(θ) = y-coordinate on unit circle

Special Angles

Degrees	Radians	Sine (Exact)	Sine (Decimal)
0°	0	0	0
30°	π/6	1/2	0.5
45°	π/4	√2/2	0.7071
60°	π/3	√3/2	0.8660
90°	π/2	1	1
180°	π	0	0
270°	3π/2	-1	-1
360°	2π	0	0

Sine Function Properties

Domain & Range

Domain: All real numbers

Range: [-1, 1]

Periodicity

Period: 2π radians (360°)

sin(x + 2π) = sin(x)

Symmetry

Odd function: sin(-x) = -sin(x)

Point symmetric about origin

Key Values

Maximum: 1 (at 90°, 450°, ...)

Minimum: -1 (at 270°, 630°, ...)

Frequently Asked Questions

The sine function (sin) is a trigonometric function that relates an angle in a right triangle to the ratio of the opposite side to the hypotenuse. It's also defined using the unit circle.

Tips

Enter the dimensions in the same unit for consistency.
Results update automatically as you type.
Use the unit selector to convert between different measurement systems.