Angular Velocity Converter - Convert rad/s, deg/s, RPM & More Units
Result:
1 rad/s = 9.54929659 RPM
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What is Angular Velocity?
Angular velocity is how fast something spins or rotates around a point. Think of a spinning wheel or a rotating fan blade. The angular velocity tells us how many degrees or radians the object turns in one second.
When you see a car engine running at 3000 RPM, that means the engine shaft makes 3000 complete turns every minute. This is angular velocity measured in revolutions per minute.
Angular velocity is different from regular speed. Regular speed tells us how fast something moves in a straight line. Angular velocity tells us how fast something rotates around a center point.
Common Angular Velocity Units
Radians per Second (rad/s)
This is the standard unit in physics and engineering. One radian equals about 57.3 degrees.
Degrees per Second (deg/s)
Easy to understand unit. Shows how many degrees something turns in one second.
Revolutions per Minute (RPM)
Very common in everyday life. Used for car engines, fans, and motors.
Revolutions per Second (rev/s)
Shows complete turns per second. Useful for very fast rotating objects.
Gradians per Second (grad/s)
Less common unit where a full circle equals 400 gradians instead of 360 degrees.
How Angular Velocity Conversion Works
Input Value
Enter angular velocity
Convert to rad/s
Use conversion factor
Convert to Target
Apply target factor
Angular Velocity Formulas
Basic Conversions
RPM to rad/s: rad/s = RPM ร (2ฯ/60)
rad/s to RPM: RPM = rad/s ร (60/2ฯ)
deg/s to rad/s: rad/s = deg/s ร (ฯ/180)
rad/s to deg/s: deg/s = rad/s ร (180/ฯ)
Physics Relations
Angular Velocity: ฯ = dฮธ/dt
Linear Velocity: v = ฯ ร r
Period Relation: ฯ = 2ฯ/T
Frequency Relation: ฯ = 2ฯf
Angular Velocity Conversion Table
| rad/s | deg/s | RPM | rev/s |
|---|---|---|---|
| 0.1 | 5.73 | 0.95 | 0.0159 |
| 0.5 | 28.65 | 4.77 | 0.0796 |
| 1 | 57.30 | 9.55 | 0.1592 |
| 2 | 114.59 | 19.10 | 0.3183 |
| 5 | 286.48 | 47.75 | 0.7958 |
| 10 | 572.96 | 95.49 | 1.5915 |
| 15 | 859.44 | 143.24 | 2.3873 |
| 20 | 1145.92 | 190.99 | 3.1831 |
| 25 | 1432.39 | 238.73 | 3.9789 |
| 30 | 1718.87 | 286.48 | 4.7746 |
| 50 | 2864.79 | 477.46 | 7.9577 |
| 75 | 4297.18 | 716.20 | 11.9366 |
| 100 | 5729.58 | 954.93 | 15.9155 |
| 150 | 8594.37 | 1432.39 | 23.8732 |
| 200 | 11459.16 | 1909.86 | 31.8310 |
Practice Problems
Problem 1:
Convert 1800 RPM to rad/s
Solution: 1800 ร (2ฯ/60) = 188.5 rad/s
Problem 2:
Convert 10 rad/s to RPM
Solution: 10 ร (60/2ฯ) = 95.49 RPM
Problem 3:
Convert 360 deg/s to rad/s
Solution: 360 ร (ฯ/180) = 6.283 rad/s
Problem 4:
Convert 5 rev/s to RPM
Solution: 5 ร 60 = 300 RPM
Problem 5:
Convert 2ฯ rad/s to deg/s
Solution: 2ฯ ร (180/ฯ) = 360 deg/s
Real World Examples of Angular Velocity
Car Engines
Most car engines run between 800-6000 RPM. At highway speeds, your engine might spin at 2500 RPM. This means the crankshaft makes 2500 complete turns every minute.
Washing Machines
During the spin cycle, washing machines can reach 1200-1600 RPM. This high angular velocity helps remove water from your clothes.
Computer Hard Drives
Traditional hard drives spin at 5400 or 7200 RPM. Faster spinning means quicker data access, which makes your computer run faster.
Wind Turbines
Wind turbine blades rotate slowly at about 20-40 RPM. Even though this seems slow, the blade tips move very fast because the blades are so long.
Ceiling Fans
Ceiling fans typically run at 100-300 RPM. Higher speeds create more air movement but also use more electricity.
Centrifuges
Medical centrifuges can spin at 15000 RPM or more. This extreme angular velocity separates blood components by weight.
How to Convert Angular Velocity Units
Step-by-Step Conversion Process
- First, identify what unit you have and what unit you want
- Find the conversion factor between these units
- Multiply your original value by the conversion factor
- Check if your answer makes sense
Converting RPM to rad/s
To convert from RPM to radians per second:
rad/s = RPM ร (2ฯ รท 60)
Example: 1800 RPM = 1800 ร 0.1047 = 188.5 rad/s
Converting deg/s to rad/s
To convert from degrees per second to radians per second:
rad/s = deg/s ร (ฯ รท 180)
Example: 360 deg/s = 360 ร 0.0175 = 6.28 rad/s
Common Angular Velocity Conversions
Low Speed Examples
1 RPM = 0.105 rad/s = 6 deg/s
10 RPM = 1.05 rad/s = 60 deg/s
60 RPM = 6.28 rad/s = 360 deg/s
Typical for: Clock hands, slow fans
Medium Speed Examples
1000 RPM = 104.7 rad/s = 6000 deg/s
1500 RPM = 157.1 rad/s = 9000 deg/s
3000 RPM = 314.2 rad/s = 18000 deg/s
Typical for: Car engines, power tools
High Speed Examples
7200 RPM = 753.8 rad/s = 43200 deg/s
10000 RPM = 1047.2 rad/s = 60000 deg/s
15000 RPM = 1570.8 rad/s = 90000 deg/s
Typical for: Hard drives, turbines
Why Angular Velocity Matters
In Engineering
- โขEngineers need to know how fast machine parts rotate to prevent breakage
- โขMotor speed affects power output and efficiency
- โขBalancing rotating parts requires precise angular velocity calculations
In Daily Life
- โขCar tachometers show engine RPM to help you drive efficiently
- โขWashing machine spin speeds determine how dry your clothes get
- โขFan speeds control air circulation and energy use
Frequently Asked Questions
What is the difference between angular velocity and linear velocity?
Linear velocity measures how fast something moves in a straight line (like miles per hour). Angular velocity measures how fast something rotates around a point (like RPM). A spinning wheel has angular velocity, while a car driving straight has linear velocity.
Why do we use different units for angular velocity?
Different industries prefer different units. Car mechanics use RPM because it's easy to understand. Scientists use rad/s because it works better with physics formulas. Engineers might use deg/s when working with angles.
How do I convert RPM to rad/s quickly?
Multiply RPM by 0.1047. This works because 2ฯ/60 โ 0.1047. For example: 3000 RPM ร 0.1047 = 314.1 rad/s. This is close enough for most practical purposes.
What happens if something spins too fast?
Every rotating object has a maximum safe angular velocity. Beyond this limit, centrifugal forces can cause the object to break apart. This is why car engines have rev limiters and why washing machines are balanced.
Can angular velocity be negative?
Yes! Negative angular velocity just means the object is rotating in the opposite direction. If we say clockwise is positive, then counterclockwise would be negative. The magnitude tells us how fast it spins.