Enter a cosine value between -1 and 1 into the Arccos Calculator to find the inverse cosine (arccos) of that number. You get back the angle in degrees and angle in radians instantly — perfect for trigonometry, physics, and engineering problems.
Angle in Degrees
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Angle in Radians
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Angle in Gradians
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Arccos, written as arccos(x) or cos⁻¹(x), is the inverse of the cosine function. It returns the angle whose cosine equals a given value. For example, arccos(0.5) = 60° because cos(60°) = 0.5. The input must be between -1 and 1, and the result falls in the range 0° to 180°.
The domain of arccos(x) is [-1, 1] — you can only input values between -1 and 1 inclusive. The range (the output angles) is [0°, 180°] in degrees, or [0, π] in radians. Values outside the domain are undefined for real numbers.
To find arccos(x), use the formula: angle = arccos(x) = cos⁻¹(x). On a scientific calculator, enter the value and press the cos⁻¹ or arccos button. In programming languages, use Math.acos(x) which returns the result in radians. To convert to degrees, multiply by (180/π).
These are two completely different things. cos⁻¹(x) (arccos) is the inverse cosine function that returns an angle. The notation 1/cos(x) is the reciprocal of cosine, which equals the secant function sec(x). Always interpret cos⁻¹(x) as arccos, not as a reciprocal.
To convert radians to degrees, multiply the radian value by (180/π ≈ 57.2958). For example, arccos(0.5) = π/3 radians × (180/π) = 60°. To go the other way, multiply degrees by (π/180) to get radians.
Arccos is used in many fields. In physics, it calculates the angle between two vectors using the dot product formula. In construction and ergonomics, it determines angles of inclination or tilt. In computer graphics, it finds the angle of rotation. In navigation, it helps compute bearing angles.
The cosine function only produces values in the range [-1, 1] for all real angles. Therefore, its inverse — arccos — can only accept inputs in that same range. If you input a value outside [-1, 1], there is no real angle whose cosine equals that value, making the result undefined in the real number system.
These are key reference values: arccos(0) = 90° (π/2 rad), arccos(1) = 0° (0 rad), and arccos(-1) = 180° (π rad). These correspond to the endpoints and midpoint of the arccos function's range and are commonly used in trigonometry problems.