RPM Calculator
Calculate revolutions per minute, linear speed, pulley RPM, gear ratio RPM, machining spindle speed, wheel RPM, Hz, rad/s, and degrees per second.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the RPM use case, solve mode, and preferred output units.
Enter the known values
Fill in the visible fields. The calculator updates automatically.
Visual demonstration
The diagram updates based on the selected RPM calculation type.
Solution
Live result, equivalent values, warnings, assumptions, and full calculation steps.
Quick checks
- RPM—
- Frequency—
- Angular velocity—
- Linear speed—
- Circumference—
Source, standards, and assumptions
Source/standard: Standard engineering formula or educational calculation method. No single governing code standard is required for this simplified RPM calculation.
Show solution steps See the governing equation, unit conversions, substitutions, and practical interpretation.
- Enter values to see the full calculation steps and checks.
What Is RPM?
RPM stands for revolutions per minute. It measures how many complete rotations an object makes in one minute. RPM is used for motors, wheels, shafts, pulleys, gears, fans, drills, lathes, milling cutters, engines, rollers, and other rotating equipment.
RPM describes rotational speed, not linear speed. A small wheel and a large wheel can spin at the same RPM, but the larger wheel has a faster outside-edge speed because it travels a greater distance each revolution. That is why diameter matters when converting RPM to surface speed, wheel speed, belt speed, or vehicle speed.
In engineering and physics, rotational motion may also be described using frequency in hertz or angular velocity in radians per second. RPM remains common in rotating machinery because it is easy to read on motor nameplates, tachometers, machining charts, vehicle calculations, and mechanical equipment specifications. For formal SI unit guidance, see the NIST Guide to the SI.
RPM Formula
The basic RPM formula divides the number of revolutions by the elapsed time in minutes. If the time is given in seconds, convert seconds to minutes before calculating RPM.
Basic RPM Equation
Where N is the number of complete revolutions and tmin is time in minutes.
Reverse Forms
Use these forms when solving for total revolutions or elapsed time instead of RPM.
Count the revolutions
Use the number of complete turns. One revolution means one full 360-degree rotation.
Convert time to minutes
RPM means revolutions per minute, so seconds must be divided by 60 before using the formula.
Divide revolutions by minutes
The result is the average rotational speed over the time interval being measured.
Example
If a shaft makes 120 revolutions in 15 seconds, then 15 seconds equals 0.25 minutes. The RPM is \(120 / 0.25 = 480\). The shaft is rotating at 480 RPM.
RPM Conversions: Hz, rad/s, and Degrees per Second
RPM is commonly converted to hertz, radians per second, revolutions per second, and degrees per second. These conversions are useful when moving between machine-speed values and physics or controls equations.
RPM to Frequency
Hertz means cycles per second. For rotational motion, 1 Hz equals 1 revolution per second.
RPM to Angular Velocity
Angular velocity is usually written as \(\omega\) and measured in radians per second.
RPM to Degrees per Second
One revolution is 360 degrees, and one minute is 60 seconds, so each RPM equals 6 degrees per second.
| RPM | Hz | rad/s | deg/s |
|---|---|---|---|
| 60 | 1 | 6.283 | 360 |
| 100 | 1.667 | 10.472 | 600 |
| 1,000 | 16.667 | 104.72 | 6,000 |
| 3,600 | 60 | 376.99 | 21,600 |
RPM to Linear Speed
RPM only tells you how fast an object rotates. Linear speed tells you how fast a point on the outside edge moves. To convert RPM to linear speed, multiply the circumference by the number of revolutions per minute.
General Formula
Use this form when \(D\) is diameter and \(v\) is linear speed in distance per second.
Feet per Minute with Diameter in Inches
This is useful for rollers, conveyors, belts, wheels, feed systems, and rotating equipment where diameter is measured in inches.
Miles per Hour with Diameter in Inches
This version is useful when converting wheel RPM to road speed.
Common mistake
Do not use radius when the formula asks for diameter. If you only know radius, multiply it by 2 first: \(D = 2r\).
How to Calculate RPM from Linear Speed
Sometimes you know the target linear speed and need to calculate the required RPM. This is common for conveyor rollers, drive wheels, feed rollers, tires, and rotating drums.
General Reverse Formula
Use this when speed is in distance per second and diameter is in the same length unit.
Feet per Minute and Inches
This form is practical for conveyor and roller calculations.
Substitute the Values
Result
Required rotational speed: approximately 318.3 RPM
Pulley RPM Formula
Pulley RPM calculations are based on the idea that the belt surface speed is the same at the driver and driven pulley when there is no slip. A larger driven pulley reduces output RPM, while a smaller driven pulley increases output RPM.
Basic Pulley Speed Relationship
The product of RPM and pulley diameter is equal on both sides of an ideal belt drive.
Driven Pulley RPM
Where \(RPM_1\) is driver RPM, \(D_1\) is driver diameter, \(RPM_2\) is driven RPM, and \(D_2\) is driven diameter.
Calculation
Result
Driven pulley speed: 875 RPM
Practical pulley notes
Use effective pulley diameter or pitch diameter when that is the correct design value. Real belt systems can differ from the ideal result due to belt slip, belt stretch, pulley wear, load changes, wrap angle, and belt tension.
Gear Ratio RPM Formula
Gear RPM calculations relate input speed, output speed, and gear ratio. A reduction ratio lowers output RPM and ideally increases torque before losses. A speed-increase ratio raises output RPM and ideally reduces torque before losses.
Output RPM from Reduction Ratio
\(R\) is the reduction ratio. For example, a 3:1 reducer divides input RPM by 3.
Output RPM from Gear Teeth
\(T_{driver}\) is the number of teeth on the input gear and \(T_{driven}\) is the number of teeth on the output gear.
Calculation
Result
Output speed: 600 RPM
| Gear Situation | Output RPM | Ideal Torque Effect | Practical Note |
|---|---|---|---|
| Reduction ratio greater than 1:1 | Lower than input RPM | Higher output torque before losses | Common in gearboxes and reducers |
| Ratio equal to 1:1 | Same as input RPM | No ideal torque change | Speed transfer only |
| Speed increase ratio below 1:1 | Higher than input RPM | Lower output torque before losses | Check gear rating and speed limits |
Machining and Spindle RPM Formula
Machining RPM calculations estimate spindle speed from cutting speed and tool or workpiece diameter. This is commonly used for drilling, milling, turning, boring, facing, and lathe work.
General Cutting Speed Relationship
\(V_c\) is cutting speed and \(D\) is tool or workpiece diameter. Units must be consistent.
Metric Form
Use this when cutting speed is in m/min and diameter is in millimeters.
Imperial SFM Shortcut
This is a common shop formula when cutting speed is in surface feet per minute and diameter is in inches.
Calculation
Result
Recommended starting spindle speed: approximately 2,292 RPM
Machining warning
This is a theoretical spindle-speed estimate. Final RPM depends on material, tool material, tool coating, chip load, coolant, workholding, tool overhang, machine rigidity, and manufacturer recommendations.
Vehicle, Wheel, and Engine RPM Formula
Vehicle RPM calculations relate road speed, tire diameter, wheel RPM, transmission ratio, and final drive ratio. The first step is calculating wheel RPM from speed and tire circumference. Engine RPM is then estimated by multiplying wheel RPM by the drivetrain ratios.
Wheel RPM from Vehicle Speed
Use consistent units for vehicle speed and tire diameter.
Engine RPM
\(R_t\) is transmission ratio and \(R_f\) is final drive ratio.
Common MPH and Tire Diameter Shortcut
This shortcut estimates wheel RPM from road speed in mph and tire diameter in inches.
Wheel RPM
Engine RPM
Result
Estimated engine speed: approximately 2,182 RPM
Vehicle RPM assumptions
The calculation assumes no tire slip, no clutch slip, no torque converter slip, no tire growth, exact drivetrain ratios, and a tire diameter that represents the loaded rolling condition.
RPM vs Linear Speed vs Angular Velocity
RPM, linear speed, frequency, and angular velocity describe related but different parts of rotating motion. Understanding the difference helps prevent wrong formulas and wrong units.
| Term | What It Means | Common Units | Depends on Diameter? |
|---|---|---|---|
| RPM | Rotations per minute | RPM, rev/min | No |
| Frequency | Rotations or cycles per second | Hz, rev/s | No |
| Angular velocity | Angular change per second | rad/s, deg/s | No |
| Linear speed | Speed at the outside edge or surface | ft/min, m/s, mph | Yes |
Simple way to remember it
RPM tells how fast something spins. Linear speed tells how fast the edge moves. Two parts can have the same RPM but different linear speeds if their diameters are different.
Common RPM Applications
RPM calculations show up anywhere rotating parts are used. The correct formula depends on whether the user cares about rotational speed, surface speed, output speed, belt speed, spindle speed, or vehicle speed.
Motors and Shafts
Used for motor nameplates, shaft speed, fan speed, pump speed, and rotating equipment checks.
Wheels and Rollers
Used for tire speed, conveyor rollers, print rollers, feed wheels, and surface-speed calculations.
Pulleys and Belts
Used for compressors, fans, pumps, machinery, and belt-driven speed changes.
Gears and Gearboxes
Used for reducers, speed increasers, gear trains, and torque-speed tradeoffs.
Machining
Used for drilling, milling, turning, lathes, tool speed, and spindle speed selection.
Engines and Vehicles
Used for road speed, gear ratios, tire diameter, final drive ratio, and engine operating RPM.
Common RPM Calculation Mistakes
Many RPM errors come from using the right equation with the wrong units, wrong diameter, or wrong physical assumption. The checklist below covers the most common issues.
Common Don’ts
- Use radius when the formula requires diameter.
- Forget to convert seconds to minutes before calculating RPM.
- Mix inches, feet, meters, seconds, and minutes without converting units.
- Confuse RPM with radians per second.
- Ignore belt slip, tire slip, clutch slip, or torque converter slip.
- Use unloaded tire diameter when loaded rolling diameter is more appropriate.
- Treat machining RPM as final tooling advice instead of a starting estimate.
- Assume every gear ratio reduces speed.
Better Checks
- Confirm whether the formula needs radius or diameter.
- Convert time to minutes for basic RPM calculations.
- Keep all length and speed units consistent.
- Use rad/s for physics equations and RPM for rotating machine speed.
- Add realistic slip assumptions when the system requires it.
- Use effective pulley diameter, pitch diameter, or loaded tire diameter when appropriate.
- Verify machining RPM with tooling and manufacturer guidance.
- Check whether the gear set is reducing speed or increasing speed.
Quick Reference RPM Formulas
Use this table as a compact RPM formula reference. The calculator above applies these relationships automatically based on the selected calculation type.
| Use Case | Formula | What It Calculates |
|---|---|---|
| Basic RPM | \(RPM = N / t_{min}\) | RPM from revolutions and time |
| Hz from RPM | \(Hz = RPM / 60\) | Rotational frequency |
| rad/s from RPM | \(\omega = RPM \cdot 2\pi / 60\) | Angular velocity |
| deg/s from RPM | \(deg/s = RPM \cdot 6\) | Angular speed in degrees per second |
| Linear speed | \(v = \pi D \cdot RPM / 60\) | Surface speed from RPM and diameter |
| RPM from speed | \(RPM = 60v / \pi D\) | Required RPM for target linear speed |
| Pulley RPM | \(RPM_2 = RPM_1D_1 / D_2\) | Driven pulley speed |
| Gear output RPM | \(RPM_{out} = RPM_{in} / R\) | Output speed from gear ratio |
| Gear teeth RPM | \(RPM_{out} = RPM_{in}T_{driver}/T_{driven}\) | Output speed from tooth counts |
| Spindle RPM | \(RPM = V_c / \pi D\) | Machining spindle speed |
| SFM spindle RPM | \(RPM = 3.82 \cdot SFM / D_{in}\) | Imperial machining RPM estimate |
| Wheel RPM | \(RPM_{wheel} = MPH \cdot 336 / D_{in}\) | Wheel RPM from vehicle speed |
| Engine RPM | \(RPM_{engine} = RPM_{wheel}R_tR_f\) | Engine RPM from wheel RPM and ratios |
Worked Examples
The examples below match the most common RPM calculator use cases: revolutions and time, surface speed, pulley reduction, gear reduction, spindle speed, and engine RPM.
Revolutions and Time
120 revolutions in 15 seconds equals \(120 / 0.25 = 480\). The rotational speed is 480 RPM.
RPM to Surface Speed
A 10-inch roller at 1,000 RPM has a surface speed of \(\pi \cdot 10 \cdot 1000 / 12\), or about 2,618 ft/min.
Pulley Reducer
A 1,750 RPM motor with a 4-inch driver pulley and 8-inch driven pulley gives \(1750 \cdot 4 / 8 = 875\). The driven pulley speed is 875 RPM.
Gear Reducer
A 1,800 RPM input through a 3:1 reducer gives \(1800 / 3 = 600\). The output speed is 600 RPM.
Spindle RPM
For 300 SFM and a 0.5-inch tool, \(RPM = 3.82 \cdot 300 / 0.5\). The starting spindle speed is approximately 2,292 RPM.
Engine RPM
At 65 mph with a 28-inch tire, 0.75 transmission ratio, and 3.73 final drive, the estimated engine speed is approximately 2,182 RPM.
Frequently Asked Questions
How do you calculate RPM?
RPM is calculated by dividing the number of revolutions by the elapsed time in minutes. The basic formula is \(RPM = revolutions / minutes\).
What is the formula for RPM?
The basic RPM formula is \(RPM = N / t_{min}\), where \(N\) is the number of revolutions and \(t_{min}\) is time in minutes.
How do you convert RPM to Hz?
Divide RPM by 60. For example, 1,800 RPM equals 30 Hz because \(1800 / 60 = 30\).
How do you convert RPM to rad/s?
Multiply RPM by \(2\pi / 60\). For example, 1,000 RPM is approximately 104.72 rad/s.
How do you convert RPM to linear speed?
Use \(v = \pi D \cdot RPM / 60\), where \(D\) is diameter. The outside edge moves one circumference per revolution.
Why does diameter matter when converting RPM to speed?
Diameter controls circumference. A larger diameter travels farther in one revolution, so it has a higher linear speed at the same RPM.
How do you calculate pulley RPM?
For an ideal belt drive, use \(RPM_2 = RPM_1D_1 / D_2\). The driven RPM equals driver RPM multiplied by driver diameter divided by driven diameter.
How do you calculate gear output RPM?
Divide input RPM by the reduction ratio. You can also use tooth counts with \(RPM_{out} = RPM_{in}T_{driver}/T_{driven}\).
How do you calculate spindle RPM from SFM?
Use \(RPM = 3.82 \cdot SFM / D_{in}\), where SFM is surface feet per minute and \(D_{in}\) is tool or workpiece diameter in inches.
How do you calculate engine RPM from speed?
Calculate wheel RPM from speed and tire diameter, then multiply by transmission ratio and final drive ratio. A common shortcut is \(RPM_{wheel} = MPH \cdot 336 / D_{in}\).
Is RPM the same as angular velocity?
No. RPM is revolutions per minute. Angular velocity is often measured in radians per second. They describe related rotational motion but use different units.
Can real-world RPM differ from the calculator result?
Yes. Belt slip, tire slip, clutch slip, torque converter slip, tool loading, bearing losses, tire deflection, and measurement assumptions can all affect real systems.