Example 1 — 30°
- Mode: from angle
- 30°
0.5
The classic school value.
Sine of an angle
Enter an angle or the sides of a right triangle — get sine. Use degrees or radians.
Sine is a number from −1 to 1. In a right triangle: sin = opposite ÷ hypotenuse.
Result
Choose a mode and fill in the inputs.
How it works
Sine measures how steep an angle is relative to the hypotenuse. In a right triangle: sin α = opposite / hypotenuse.
For degrees the calculator converts to radians first (× π/180), then takes sine. Known values: sin 0° = 0, sin 30° = 0.5, sin 90° = 1.
Everyday use: slope of a ramp, roof pitch, or aiming up at a given angle.
Formula
From angle: sin α (degrees or radians)
From sides: sin α = opposite ÷ hypotenuse
How to use this calculator
- Choose: from an angle or from sides.
- For an angle, set degrees or radians and enter the value.
- For sides, enter opposite and hypotenuse.
- Try the examples — 30° and a 3-5 pair are a good start.
Examples
Example 2 — 90°
- 90°
1
Largest sine in the 0°–90° range.
Example 3 — π/2 radians
- Unit: radians
- ≈ 1.5708
1
Same angle as 90°.
Example 4 — sides 3 and 5
- Opposite: 3
- Hypotenuse: 5
0.6
3/5 = 0.6 — common with a 3-4-5 triangle.
Frequently asked questions
Degrees or radians?
School problems usually use degrees (30°, 45°, 60°). Many science formulas default to radians. Match whatever your question uses.
Why is sin 30° equal to 0.5?
An equilateral triangle split by a height makes two 30-60-90 triangles. The side opposite 30° is half the hypotenuse, so the ratio is 1/2.
Can sine be greater than 1?
Not from an angle alone. If sides give a value above 1, they cannot form a right triangle (opposite longer than hypotenuse).
What is the opposite side?
The side that does not touch the angle you care about — it sits across from it. The hypotenuse is always the longest side at the right angle.
Does sin(−30°) make sense?
Yes — sine is odd: sin(−α) = −sin α. For example sin(−30°) = −0.5.
Why offer a sides mode?
Sometimes you only know lengths. Or you measure on a sketch and want sine quickly.
How do I remember sine vs cosine?
Sine uses the opposite side; cosine uses the adjacent side (next to the angle). Both divide by the hypotenuse.
Do 180° and 0° give the same sine?
sin 0° = 0 and sin 180° = 0 — same value, different place on the unit circle.