Enter values to see results
—
°
—
—
—
Enter values to see results
—
°
—
—
—
The Radians to Degrees Converter converts radian measurements to degrees with high precision. This conversion is essential when translating results from scientific calculations, programming output, or mathematical formulas into the degree format that is more intuitive for everyday use, navigation, and engineering drawings.
The formula is: degrees = radians × 180 / pi. Since a full circle is 2pi radians = 360 degrees, the conversion factor is 180/pi ≈ 57.2957795. Our converter provides both decimal degrees and DMS (degrees-minutes-seconds) format, which is used in navigation, surveying, and geographic coordinate systems.
Radians are the natural unit of angular measure in mathematics and physics because they represent the ratio of arc length to radius. However, degrees are far more common in everyday contexts: compass bearings, architectural drawings, sports angles, and weather wind directions all use degrees. Converting from radians to degrees bridges the gap between mathematical computation and practical communication.
The DMS output is particularly valuable for GPS coordinates (e.g., 40° 26' 46" N), astronomical observations, and land surveying. Each degree contains 60 arc minutes, and each arc minute contains 60 arc seconds, providing fine angular resolution.
The formula: degrees = radians × 180 / pi. For DMS conversion: whole degrees are the integer part; minutes = fractional part × 60 (integer part); seconds = remaining fraction × 60.
Key references: pi rad = 180°, pi/2 rad = 90°, pi/4 rad = 45°, 1 rad ≈ 57.296°. When reading scientific papers, angles in formulas are almost always in radians unless explicitly stated otherwise.
Inputs
Results
pi ≈ 180°
Inputs
Results
1 rad ≈ 57° 17' 45"
Degrees = Radians × 180 / pi. Equivalently, multiply radians by approximately 57.2957795.
1 radian = 180/pi ≈ 57.2958 degrees, or 57° 17' 44.8".
pi/2 radians = 90 degrees exactly. This is a right angle.
2pi radians = 360 degrees exactly. This is a full rotation.
DMS stands for Degrees-Minutes-Seconds. 1 degree = 60 minutes, 1 minute = 60 seconds. Example: 45.5° = 45° 30' 0".
Use the DEGREES() function: =DEGREES(radians). For example, =DEGREES(PI()) returns 180.
Math libraries (JavaScript, Python, C/C++) use radians because they simplify trigonometric computations. The derivative d/dx sin(x) = cos(x) only holds when x is in radians.
Yes. Negative radians produce negative degrees: -pi/2 rad = -90°. Negative angles indicate clockwise rotation from the positive x-axis.
pi/6 radians = 30 degrees. This is one of the standard angles in trigonometry (30-60-90 triangle).
Results are computed to floating-point precision (about 15-16 significant digits), then displayed to 6 decimal places for degrees and 2 for DMS seconds.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
