Cosine CalculatorFree online math calculator — instant results, no sign-up
Calculate the cosine of an angle in degrees.
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About the Cosine Calculator
The Cosine Calculator calculates the cosine of an angle entered in degrees. It converts the angle to radians for evaluation and returns a dimensionless value between −1 and 1. With the default angle of 60 degrees, the result is 0.5.
- Angle (degrees)
- The angle whose cosine you want to calculate, measured in degrees and set to 60 by default.
Formula and method
r = cos(θ × π / 180); for θ = 60, r = cos(60 × π / 180) = cos(π / 3) = 0.5.
- rThe cosine result, a dimensionless number between −1 and 1.
- θThe input angle measured in degrees.
- πPi, the mathematical constant used in the conversion from degrees to radians.
Multiply the degree input by π / 180 to convert it to radians, then evaluate the cosine of that radian angle. For the default input, 60 degrees becomes π / 3 radians, whose cosine is exactly 0.5.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Angle (degrees)60
Results
- Result0.5
How to use the Cosine Calculator
- 1Locate the Angle (degrees) input.
- 2Keep the default value of 60 to follow the worked example, or enter your desired angle in degrees.
- 3Run the calculation to evaluate the cosine of the entered angle.
- 4Read the Result row; with the default input of 60, it shows 0.5.
Reading your result
The Result row gives the cosine of the input angle, not an angle in degrees or radians. For 60 degrees, Result = 0.5 means that the adjacent side divided by the hypotenuse of a right triangle with that angle is 0.5. More generally, cosine is the horizontal coordinate of the corresponding point on the unit circle.
Limitations
The input is interpreted as degrees, so a radian value must be converted to degrees before entry. Cosine is defined for every finite real angle, including negative angles and angles beyond a full turn. Numerical evaluation and display rounding can introduce small errors, especially for extremely large angle inputs; the default result of 0.5 is mathematically exact.
Common questions
Why does an angle of 60 degrees give a cosine of 0.5?+
In a right triangle with a 60-degree angle, the adjacent side is half the hypotenuse. Since cosine is adjacent side divided by hypotenuse, cos(60°) = 0.5.
Can I enter an angle in radians?+
This calculator interprets the input as degrees. Convert radians to degrees by multiplying by 180 / π before entering the value.
Can cosine be negative?+
Yes. Cosine is negative when the corresponding unit-circle point lies to the left of the vertical axis, in the second and third quadrants.
How do negative angles and full turns affect the result?+
Cosine is even, so cos(−θ) = cos(θ). It also repeats every 360 degrees, so adding or subtracting a whole number of full turns leaves the mathematical result unchanged.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.