Example 1
- Mode: from angle
- 30°
0.5
The classic school value.
Sine of an angle calculator
Pick from an angle or from triangle sides. Sine runs from −1 to 1. sin 30° = 0.5, sin 90° = 1. From 3-4-5 sides: opposite 3 and hypotenuse 5 give 0.6.
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 says how steep an angle is relative to the hypotenuse. In a right triangle: sin α = opposite / hypotenuse. sin 0° = 0, sin 30° = 0.5, sin 90° = 1. From 3 and 5 you get 3/5 = 0.6.
For an angle in degrees the calculator first converts to radians (× π/180), then takes sine. π/2 rad, about 1.5708, is the same angle as 90° and also gives 1. sin 180° = 0, like sin 0°.
How do you want to compute? has From an angle and From triangle sides. For an angle set Angle unit to degrees or radians and type Angle, for example 30. For sides type Opposite side and Hypotenuse, for example 3 and 5. Click Calculate.
Cosine 60° = 0.5 is the pair of sin 30°. Hypotenuse 5 from legs 3 and 4 lives on Pythagoras. Here you know the angle or the side ratio; you are not hunting a missing side.
Without an angle in angle mode, or without both sides in sides mode, nothing computes. The hypotenuse must be positive and not shorter than the opposite side.
sin 45° ≈ 0.7071. sin 60° ≈ 0.8660. From 4 and 5 (opposite/hypotenuse) you get 0.8. Check 30° and the 3-5 pair first.
Formula
From angle: sin α (degrees or radians)
From sides: sin α = opposite ÷ hypotenuse
How to use
- Pick How do you want to compute?: From an angle or From triangle sides.
- For an angle, set degrees or radians and type the angle, for example 30.
- For sides, type the opposite side and the hypotenuse, for example 3 and 5.
- Click Calculate. 30° gives 0.5. 90° gives 1. 3 and 5 give 0.6.
- Cosine of the same angle lives on cosine. The missing 3-4-5 side lives on Pythagoras.
sin 30° = 0.5
Sine runs from −1 to 1. sin 30° = 0.5, sin 90° = 1. From 3-4-5 sides: opposite 3 and hypotenuse 5 give 0.6.
- sin
- Sine of an angle, or opposite over hypotenuse. sin 30° = 0.5. 3/5 = 0.6. sin 90° = 1.
- °
- Degrees in angle mode. 30° gives 0.5. About 1.5708 rad is the same angle as 90° and sine 1.
Examples
Example 2
- 90°
1
Largest sine in the 0° - 90° range.
Example 3
- Unit: radians
- ≈ 1.5708
1
Same angle as 90°.
Example 4
- Opposite: 3
- Hypotenuse: 5
0.6
3/5 = 0.6 - common with a 3-4-5 triangle.
Related calculators
Frequently asked questions
What is sin 30°?
0.5. The classic school value. First example on the page.
What is sin 90°?
1. The largest sine on 0°-90°. In radians π/2 gives the same.
What sine do 3 and 5 give?
0.6. That is 3/5 from a 3-4-5 triangle in sides mode, not a typed angle.
Is sin 180° the same as sin 0°?
Yes, both are 0. The calculator covers a full turn, not only an acute angle.
How do I switch to radians?
Angle unit: Radians, then type for example 1.5708 instead of 90.
What are sin 45° and sin 60°?
About 0.7071 and 0.8660. sin 60° pairs with cos 30°.
How is sine different from cosine?
Sine takes the opposite side. Cosine takes the adjacent. At 30° sine is 0.5 and cosine is about 0.866.
Can the hypotenuse be 3 when the opposite is 5?
No. The hypotenuse is longest. Opposite 5 and hypotenuse 3 do not make a triangle.
Where is c = 5 from a = 3 and b = 4?
On the Pythagorean theorem. Here 3 and 5 give the ratio 0.6, not a missing side.
Can sine be negative?
Yes, below the axis, for example sin 210° = −0.5. The range stays −1 to 1.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.