Example 1
- 60°
0.5
Pairs with sin 30° = 0.5.
Cosine of an angle calculator
Pick from an angle or from triangle sides. Cosine runs from −1 to 1. cos 60° = 0.5, cos 0° = 1, cos 90° = 0. Adjacent 4 and hypotenuse 5 give 0.8.
Cosine is from −1 to 1. In a right triangle: cos = adjacent ÷ hypotenuse.
Result
Choose a mode and fill in the inputs.
How it works
Cosine takes the side next to the angle (adjacent) and divides by the hypotenuse: cos α = adjacent / hypotenuse. Familiar values: cos 0° = 1, cos 60° = 0.5, cos 90° = 0. The closer the angle is to 90°, the closer cosine is to zero.
The pair of sin 30° = 0.5 is cos 60° = 0.5. In a 3-4-5 triangle the adjacent to one acute angle is often 4, the hypotenuse 5, ratio 0.8. Arccos 0.5 returns 60° on the inverse cosine page.
How do you want to compute? has From an angle and From triangle sides. For an angle set Angle unit and type Angle, for example 60. For sides type Adjacent side and Hypotenuse, for example 4 and 5. Click Calculate.
Sine of the same 60° is about 0.866, another calculator. Pythagoras from 3 and 4 gives c = 5, then 4/5. Here you either know the angle or you already have both sides of the ratio.
Without an angle or without both sides, nothing computes. The hypotenuse must be positive and not shorter than the adjacent side.
cos 30° ≈ 0.8660. cos 45° ≈ 0.7071. cos 180° = −1. Check 60° and 0° on the page.
Formula
From angle: cos α
From sides: cos α = adjacent ÷ 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 60.
- For sides, type the adjacent side and the hypotenuse, for example 4 and 5.
- Click Calculate. 60° gives 0.5. 0° gives 1. 4 and 5 give 0.8.
- Sine of this angle lives on sine. The angle from cosine 0.5 lives on arccos.
cos 60° = 0.5
Cosine runs from −1 to 1. cos 60° = 0.5, cos 0° = 1, cos 90° = 0. Adjacent 4 and hypotenuse 5 give 0.8.
- cos
- Cosine of an angle, or adjacent over hypotenuse. cos 60° = 0.5. 4/5 in a 3-4-5 triangle is 0.8.
- °
- Degrees in angle mode. 60° gives 0.5. 0° gives 1. 0 rad is the same as 0°.
Examples
Example 2
- 0°
1
Full adjacent component along the axis.
Example 3
- 0 rad
1
Same as 0°.
Example 4
- Adjacent: 4
- Hypotenuse: 5
0.8
4/5 = 0.8 in a 3-4-5 triangle.
Example 5
- How do you want to compute?: angle
- Angle unit: deg
- Angle: 60
0.5
What is cos 60° and cos 0°? 0.5 and 1.
Related calculators
Frequently asked questions
What is cos 60°?
0.5. The pair of sin 30° = 0.5. First example on the page.
What is cos 0°?
1. The angle along the axis, a full adjacent component. cos 90° = 0.
What cosine do 4 and 5 give?
0.8. Adjacent 4 over hypotenuse 5, a 3-4-5 triangle.
How is cosine different from sine?
Cosine takes adjacent. Sine takes opposite. At 60° cosine is 0.5 and sine is about 0.866.
What are cos 30° and cos 45°?
About 0.8660 and 0.7071. cos 30° pairs with sin 60°.
What is cos 180°?
−1. Cosine reaches minus one; the range is still [−1, 1].
Where do I recover the angle from 0.5?
On arccos. arccos(0.5) = 60°, the inverse of cos 60° in this calculator.
How do I compute in radians?
Angle unit: Radians. π/3, about 1.047, is 60° and also gives 0.5.
Can adjacent be longer than the hypotenuse?
No. The hypotenuse is longest. Adjacent 5 and hypotenuse 4 do not make a triangle.
Where is c = 5 from 3 and 4?
On Pythagoras. Here 4 and 5 give 0.8, not a missing side.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.