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The Revolutions to Degrees Converter converts rotational measurements from revolutions (complete turns) to degrees, radians, and gradians. A revolution represents one full rotation — 360 degrees, 2pi radians, or 400 gradians. This conversion is fundamental in mechanical engineering, motor control, physics, and animation.
Revolutions are the most intuitive way to express rotation: 1 revolution = one full spin. RPM (revolutions per minute) is the standard unit for rotational speed of engines, motors, fans, hard drives, and spinning machinery. A typical car engine idles at 600-1000 RPM, a washing machine spins at 800-1600 RPM, and a hard disk drive rotates at 5400-7200 RPM.
Converting revolutions to degrees is necessary when calculating the angular displacement of rotating components, programming servo motors (which accept degree inputs), setting up CNC machine tool paths, and creating rotation animations. For physics calculations involving torque, angular momentum, and rotational kinetic energy, conversion to radians is required.
Our converter provides all three major angle units simultaneously: degrees for practical measurement, radians for physics and mathematical computation, and gradians for surveying applications. Fractional revolutions are fully supported — for example, 0.25 rev = 90° (quarter turn), 0.5 rev = 180° (half turn).
The formulas: degrees = revolutions × 360, radians = revolutions × 2pi, gradians = revolutions × 400. These follow directly from the definition of a revolution as one complete rotation.
Common fractions: 1/4 rev = 90° (right angle), 1/2 rev = 180° (straight line), 3/4 rev = 270°, 1 rev = 360°. For RPM to degrees per second: deg/s = RPM × 6 (since 1 RPM = 360°/60s = 6°/s).
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1 rev = 360°
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0.25 rev = 90°
1 revolution = 360 degrees exactly. This is the definition of a full rotation.
1 revolution = 2pi radians ≈ 6.28318 radians.
RPM = revolutions per minute. It measures rotational speed. 1 RPM means one complete 360° rotation every 60 seconds.
Multiply RPM by 6. Since 1 revolution = 360° and 1 minute = 60 seconds: degrees/second = RPM × 360/60 = RPM × 6.
Multiply RPM by 2pi/60 ≈ 0.10472. This gives angular velocity in rad/s, the standard SI unit.
A quarter revolution = 0.25 × 360 = 90 degrees. This is a right angle.
Idle: 600-1000 RPM. Normal driving: 2000-3000 RPM. Redline: 6000-9000 RPM. An engine at 3000 RPM makes 50 revolutions per second.
In pure mathematics, the 'turn' (equivalent to revolution) is sometimes used as an alternative angle unit. Some mathematicians argue that tau (τ = 2π) should replace 2π, making 1 turn = τ radians.
A standard car tire (diameter ~0.66 m, circumference ~2.07 m) makes about 780 revolutions per kilometer or 1256 per mile.
Yes. Any decimal value works: 0.5 rev = 180° (half turn), 1.5 rev = 540° (one and a half turns), 2.75 rev = 990°.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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