Cosine Calculator
Get the cosine instantly.
Result
How it is calculated
The angle is read in degrees. The tool converts it to radians with θrad = θdeg × π ÷ 180 and then evaluates cos(θrad). The answer is a pure ratio with no unit, shown to 6 decimal places. Any real angle is accepted, including negative angles and angles above 360°, because cosine repeats every 360°: cos(θ) = cos(θ + 360°) and cos(−θ) = cos(θ). The result always lies between −1 and 1. An empty box gives no result. Exact values such as cos 90° print as 0.000000 because of the rounding to six places, not because the floating-point result is exactly zero.
Worked example
Find cos 37.5°. Convert to radians: 37.5 × π ÷ 180 ≈ 0.654498. The cosine of 0.654498 radians is about 0.793353, so the tool prints 0.793353. Sanity check: 37.5° lies between 30° (cos ≈ 0.866) and 45° (cos ≈ 0.707), and 0.793 is between those two, as it should be.
Common mistakes
- Typing radians into a box that expects degrees. Entering 1.5708 for a right angle gives cos of 1.5708 degrees, about 0.999624, not 0.
- Expecting an exact zero at 90° or 270°. The display shows 0.000000, which is a rounded value; do not use it as a proof of exact perpendicularity.
- Assuming a negative angle gives a negative cosine. Cosine is even, so cos(−60°) is 0.5, the same as cos(60°).
- Using the cosine when you actually have the ratio and want the angle. For that direction you need the arccosine, not this tool.
- Confusing cosine with sine. At 30° the cosine is 0.866 and the sine is 0.5; they swap at 60°, so check which ratio your triangle problem calls for.
About this calculator
Cosine is one of the three core trigonometric ratios: in a right triangle it is the length of the side adjacent to an angle divided by the hypotenuse. On the unit circle, cos(θ) is simply the x-coordinate of the point you reach after rotating θ degrees from the positive x-axis, which is why cosine values always stay between -1 and 1 and repeat every 360°. cos(0°) = 1, cos(90°) = 0, and cos(180°) = -1 are the anchor points most people remember from trigonometry class.
Beyond the classroom, cosine shows up wherever a quantity depends on the angle between two directions. Physicists use it in work and power formulas (W = F·d·cos θ), electrical engineers use it for AC power factor calculations, and 3D graphics programmers use it constantly to rotate objects and compute lighting via dot products. Surveyors and navigators rely on cosine (often through the law of cosines) to resolve triangles when only sides and one angle are known.
Give an angle in degrees and its cosine comes straight back; to go the other way, from a known cosine to the angle, use an arccos calculator.
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