RPM Calculator
Calculate rotational speed from linear speed, gear ratios, or cutting speed.
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Formulas
RPM = (Linear Speed × 60) / (π × Diameter)
Understanding RPM Calculations
RPM (Revolutions Per Minute) is a measure of rotational speed used across mechanical engineering, machining, and physics. Whether you are determining spindle speed for a lathe, calculating output speed through a gear train, or converting between linear and rotational motion, understanding RPM calculations is essential for proper machine operation and safety.
RPM Formulas
Angular velocity in radians per second is derived from RPM using: ω = RPM × 2π / 60. This value is useful for physics and engineering applications where rotational dynamics are involved.
How to Calculate RPM
Frequently Asked Questions
How do I calculate RPM?
RPM depends on what you know. For linear-to-rotational: RPM = (Linear Speed × 60) / (π × Diameter). For gear systems: RPM₂ = RPM₁ × (Teeth₁ / Teeth₂). For cutting speed: RPM = (SFM × 12) / (π × Diameter).
What is the gear ratio formula for RPM?
The gear ratio formula is: Driven RPM = Driver RPM × (Driver Teeth / Driven Teeth). A larger driven gear results in lower RPM but higher torque. A gear ratio of 2:1 means the driven gear spins at half the driver speed.
How do I convert RPM to linear speed?
Linear Speed = RPM × π × Diameter / 60. For example, a 0.1m diameter shaft at 1000 RPM: Speed = 1000 × π × 0.1 / 60 = 5.24 m/s. Remember to keep diameter and speed in consistent units.
What is SFM (Surface Feet per Minute)?
SFM is the speed at which the cutting edge of a tool moves across the workpiece surface. It's the standard measure for cutting speed in machining. Typical values: aluminum 500-1000 SFM, steel 100-300 SFM, stainless steel 50-200 SFM. RPM = (SFM × 12) / (π × Diameter_in_inches).
How do I calculate RPM from frequency?
For an AC motor, RPM = (120 × Frequency) / Number of Poles. For a 60Hz, 4-pole motor: RPM = (120 × 60) / 4 = 1800 RPM (synchronous). Actual speed is slightly less due to slip (typically 1725-1750 RPM).