Quick answer
cos(θ) = adjacent ÷ hypotenuse in a right triangle. cos(60°) = 0.5.
Enter an angle and choose degrees or radians. The calculator returns cos(θ). Use this cosine calculator to check your own figures.
Related tools: Inverse Cosine Calculator: arccos (inverse trigonometric function) with the result in degrees and radians. Cosine Rule Calculator: Apply the cosine rule to find a missing side or angle of a triangle from the sides and the included angle. Trigonometry Calculator: All six trigonometric functions of an angle.
How to use the Cosine Calculator
- Enter angle.
- Choose unit: Degrees and Radians.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Angle | A number | — |
| Unit | Choose one: Degrees; Radians | Starts at Degrees |
Formula and method
Formula
cos(θ)
IEEE-754 double precision; shown to at most 6 decimal places.
Angle is converted to radians and evaluated with IEEE-754 math functions. Values where the function is undefined are rejected.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Angle = 60; Unit = Degrees.
| Result | Value |
|---|---|
| cos(60°) | 0.5 |
Example 2
Inputs: Angle = 0; Unit = Degrees.
| Result | Value |
|---|---|
| cos(0°) | 1 |
Example 3
Inputs: Angle = 180; Unit = Degrees.
| Result | Value |
|---|---|
| cos(180°) | -1 |
The first line is the headline result (cos(60°)). IEEE-754 double precision; shown to at most 6 decimal places.
What it means
Cosine oscillates between −1 and 1 and equals the x-coordinate on the unit circle. cos 60° = 0.5 is the ratio of the side adjacent to the 60° angle to the hypotenuse in a 30-60-90 triangle.
Domain and checks
cos θ is defined for every angle; its values stay between −1 and 1. Angles may be negative or larger than 360°; they repeat every 360° (every 180° for tangent).
Related ratios
The reciprocal of cos is secant, available on its own page. Inverse functions (arcsin, arccos, arctan) turn a ratio back into an angle.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Angle: entering "x" shows "Angle must be a number." beside that field and no result.
Choosing between the Cosine Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Inverse Cosine Calculator](/math/inverse-cosine-calculator/) | value | arccos(0.5) |
| [Cosine Rule Calculator](/math/cosine-rule-calculator/) | side b, side c and included angle A | Side a |
| [Trigonometry Calculator](/math/trigonometry-calculator/) | angle and unit | sin |
| [SOHCAHTOA Calculator](/math/sohcahtoa-calculator/) | acute angle, known side length and known side is the | Opposite |
| [Reference Angle Calculator](/math/reference-angle/) | angle | Reference angle |
Background: trigonometry
In a right triangle, sin θ is the opposite side over the hypotenuse, cos θ the adjacent side over the hypotenuse and tan θ the opposite over the adjacent. Their reciprocals are cosecant, secant and cotangent. At 30° the values are sin = 0.5, cos = 0.866025 and tan = 0.577350.
Check the angle unit before you calculate: degrees convert to radians by multiplying by π/180, so 30° is about 0.5236 rad. Some values are undefined, for example tan 90°, because the cosine is zero there and the ratio would divide by zero.
Assumptions and limitations
- Undefined at some angles (for example tan 90°)
- Angles may be negative or larger than 360°
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for angle to confirm this.
Frequently asked questions
What is cos(60°)?
cos 60° = 0.5, because the side adjacent to a 60° angle is half the hypotenuse.
How do I convert degrees to radians?
Multiply by π/180; 30° is π/6 ≈ 0.5236 rad.
Which quadrants are positive?
Cosine is positive in quadrants I and IV.
Is the calculator exact?
It uses double-precision arithmetic, so values such as sin 30° appear as 0.5 up to the displayed rounding.
What does the Cosine Calculator calculate?
cos of an angle in degrees or radians. It returns cos(60°).
What formula does the Cosine Calculator use?
cos(θ). Angle is converted to radians and evaluated with IEEE-754 math functions.
What does the “Unit” option change?
It sets how the cosine is worked out. The choices are Degrees and Radians.
What is an example of a cosine result?
With angle 60 and unit Degrees, the cos(60°) is 0.5.
Related calculators
- Inverse Cosine Calculator — arccos (inverse trigonometric function) with the result in degrees and radians.
- Cosine Rule Calculator — Apply the cosine rule to find a missing side or angle of a triangle from the sides and the included angle.
- Trigonometry Calculator — All six trigonometric functions of an angle.
- SOHCAHTOA Calculator — Find the other two sides of a right triangle from one side and an acute angle.
- Reference Angle Calculator — Acute angle between the terminal side and the x-axis.
- Inverse Sine Calculator — arcsin (inverse trigonometric function) with the result in degrees and radians.
- Cosecant Calculator — csc of an angle in degrees or radians.
- Cotangent Calculator — cot of an angle in degrees or radians.
Sources
- Standard trigonometric definitions on the unit circle (NIST DLMF §4.14)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.