What the Sine Function Measures
The sine function (sin) is one of the core trigonometric functions. In a right triangle it relates an angle to the ratio of the side opposite the angle to the hypotenuse. Type any angle above and this sin calculator returns sin(x) at once, in degrees or radians.
sin(θ) = opposite / hypotenuse. On the unit circle, sin(θ) equals the y-coordinate of the point at angle θ.Key Properties
Bounded Range
Unit Circle
Periodic
How to Calculate Sine of an Angle
Enter the Angle
Type your angle value in the input field. You can enter whole numbers, decimals, or π expressions such as π/4 or 2π/3.
Choose DEG or RAD
Select DEG for degrees (the default) or RAD for radians. The input unit updates to match your choice.
Read the Result Instantly
The sin(x) value updates automatically as you type — no submit button needed. Press Enter to recalculate at any time.
View Exact & Related Values
For special angles, an exact value like √2/2 is shown. The cosecant (csc = 1/sin) appears as a related value, and a special-angles table can be expanded for reference.
Calculator Features
Degrees & Radians
Switch between DEG and RAD with one click, including support for π expressions like π/4 or 2π/3.
Exact Special Angles
Shows exact values such as 1/2, √2/2 and √3/2 for common angles instead of long decimals.
Related Cosecant
Displays the cosecant (csc = 1/sin) alongside the sine result for quick reference.
Real-Time Calculation
Results update instantly as you type, with a special-angles table you can expand anytime.
Common Sine Values
| Angle | sin value | Decimal |
|---|---|---|
| sin(0°) | 0 | 0.000 |
| sin(30°) | 1/2 | 0.500 |
| sin(45°) | √2/2 | 0.707 |
| sin(60°) | √3/2 | 0.866 |
| sin(90°) | 1 | 1.000 |
Frequently Asked Questions
How do I calculate the sine of an angle?
Enter the angle, pick DEG or RAD, and read sin(x) instantly. By hand, sine is the ratio of the side opposite the angle to the hypotenuse: sin(θ) = opposite / hypotenuse.
What is the range of the sine function?
The sine function always returns values between −1 and 1, inclusive — that is, sin(x) ∈ [−1, 1]. No angle produces a sine outside this range.
What is sin(90°)?
sin(90°) = 1. This is the maximum value of the sine function, reached when the angle points straight up on the unit circle. For reference, sin(30°) = 1/2 and sin(45°) = √2/2.
How do I enter an angle in radians?
Click the RAD button, then enter the value. You can use π expressions such as π/4 or a decimal like 3.14159. Degrees and radians give different results, so make sure the right unit is selected.
What is the cosecant shown next to the result?
The cosecant (csc) is the reciprocal of sine: csc(θ) = 1/sin(θ). It is shown as a related value so you don't have to compute it separately. When sin(θ) = 0, the cosecant is undefined (∞).
How does sine relate to cosine?
They are cofunctions: sin(x) = cos(90° − x). They also satisfy the Pythagorean identity sin²(x) + cos²(x) = 1.
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