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Angular Acceleration Converter: Convert rad/s², RPM/s, °/s², rev/s² and More

Angular acceleration describes how quickly the rotational speed of an object changes over time. It is an important measurement in mechanical engineering, robotics, automotive systems, electric motors, turbines, flywheels, machine tools, control systems, and rotational motion studies.

The standard SI unit for angular acceleration is radian per second squared (rad/s²). However, rotational calculations do not always use the same time or angle units. Depending on the application, angular acceleration may be expressed in radians per minute squared, degrees per second squared, revolutions per second squared, RPM per second, revolutions per hour per second, or other combinations.

That is where an Angular Acceleration Converter becomes useful.

The CalculatorKits Angular Acceleration Converter lets you convert angular acceleration between 22 different units, including rad/s², rad/min², rad/h², rad/d², rad/year², °/s², °/min², °/h², °/d², °/year², rev/s², rev/min², rev/h², rev/d², rev/year², rev/min·s, rev/h·s, rev/h·min, grad/s², grad/min², RPM/s, and RPM/min.

Instead of manually handling radians, revolutions, degrees, minutes, hours, days, and years, you can enter the value, choose the source unit, select the target unit, and get the converted result.

What Is Angular Acceleration?

Angular acceleration is the rate at which angular velocity changes with time.

It is commonly represented by the Greek letter α (alpha).

The SI unit of angular acceleration is radian per second squared (rad/s²). The International Bureau of Weights and Measures, BIPM, identifies rad/s² as the SI derived unit for angular acceleration.

The basic formula is:

α = Δω / Δt

where:

α = angular acceleration

Δω = change in angular velocity

Δt = change in time

For example, suppose a motor’s angular velocity increases from 20 rad/s to 80 rad/s in 3 seconds.

α = (80 − 20) ÷ 3

α = 20 rad/s²

The motor therefore has an average angular acceleration of 20 rad/s² during that period.

Angular acceleration can be positive or negative depending on the direction of rotation and the coordinate system being used.

What Is an Angular Acceleration Converter?

An Angular Acceleration Converter changes a measurement from one angular acceleration unit into another without changing the underlying physical quantity.

For example:

1 rad/s² ≈ 57.2958 °/s²

and:

1 rad/s² ≈ 0.159155 rev/s²

The second relationship is important because one complete revolution equals 2π radians.

The CalculatorKits Angular Acceleration Converter provides a wider range of units than the few commonly encountered in introductory physics. Its unit selection includes different angle measurements combined with seconds, minutes, hours, days, and years, as well as mixed time units such as rev/min·s and rev/h·min.

This makes it useful when working with specifications or calculations that do not use the standard rad/s² format.

How to Use the Angular Acceleration Converter

Using the CalculatorKits converter is simple.

1. Enter the angular acceleration value.
2. Select the unit of the value you already have.
3. Select the unit you want to convert to.
4. Read the converted result.
5. Use the result in your calculation or technical work.

For example, suppose you have:

100 RPM/s

and need the value in:

rad/s²

Select RPM/s as the input unit and rad/s² as the output unit.

The conversion is:

100 RPM/s ≈ 10.472 rad/s²

The calculator handles the conversion automatically.

Angular Acceleration Formula

The fundamental angular acceleration equation is:

α = Δω / Δt

For constant angular acceleration, another useful equation is:

ω = ω₀ + αt

where:

ω = final angular velocity

ω₀ = initial angular velocity

α = angular acceleration

t = elapsed time

Rearranging the equation gives:

α = (ω − ω₀) / t

For example, a rotating shaft increases from 100 rad/s to 300 rad/s in 5 seconds.

α = (300 − 100) / 5

α = 40 rad/s²

So the average angular acceleration is 40 rad/s².

Why rad/s² Is the Standard Unit

Radians and seconds are particularly useful in rotational mechanics because angular velocity and angular acceleration fit naturally into rotational equations.

BIPM identifies:

Angular velocity = rad/s

Angular acceleration = rad/s²

The same SI framework identifies acceleration as m/s² and torque as N·m.

Using rad/s² also makes the connection between angular velocity and angular acceleration straightforward:

α = dω/dt

When an object’s angular velocity changes by a certain number of radians per second during each second, the resulting rate is expressed in radians per second squared.

The 22 Angular Acceleration Units in CalculatorKits

The CalculatorKits tool groups its units into several useful families.

Radian Based Units

The converter includes:

Unit	Meaning
rad/s²	radians per second squared
rad/min²	radians per minute squared
rad/h²	radians per hour squared
rad/d²	radians per day squared
rad/year²	radians per year squared

These units all measure angular acceleration using radians while changing the time scale.

The most important one is rad/s², because it is the SI unit.

For example:

1 rad/min² = 1/3600 rad/s²

Therefore:

1 rad/min² ≈ 0.000277778 rad/s²

The difference comes from the fact that one minute contains 60 seconds and the time is squared.

Degree Based Units

The converter also includes:

Unit	Meaning
°/s²	degrees per second squared
°/min²	degrees per minute squared
°/h²	degrees per hour squared
°/d²	degrees per day squared
°/year²	degrees per year squared

Degrees are commonly used when angular position and rotational movement are described in degrees rather than radians.

The fundamental relationship is:

180° = π rad

Therefore:

1° = π/180 rad

For angular acceleration:

1 °/s² ≈ 0.0174533 rad/s²

and:

1 rad/s² ≈ 57.2958 °/s²

Example

Convert 100 °/s² to rad/s².

100 × π/180 = 1.74533 rad/s²

Therefore:

100 °/s² ≈ 1.74533 rad/s²

Revolution Based Units

The converter includes five revolution based units:

Unit	Meaning
rev/s²	revolutions per second squared
rev/min²	revolutions per minute squared
rev/h²	revolutions per hour squared
rev/d²	revolutions per day squared
rev/year²	revolutions per year squared

A revolution represents one complete rotation.

The relationship between revolutions and radians is:

1 revolution = 2π radians

Therefore:

1 rev/s² = 2π rad/s²

So:

1 rev/s² ≈ 6.28319 rad/s²

Conversely:

1 rad/s² ≈ 0.159155 rev/s²

This distinction is important because it is easy to accidentally reverse the conversion factor.

rev/s² to rad/s²

To convert revolutions per second squared to radians per second squared:

rad/s² = rev/s² × 2π

For example:

5 rev/s² × 2π = 31.4159 rad/s²

Therefore:

5 rev/s² ≈ 31.416 rad/s²

rad/s² to rev/s²

To convert radians per second squared to revolutions per second squared:

rev/s² = rad/s² ÷ 2π

For example:

10 rad/s² ÷ 2π = 1.59155 rev/s²

Therefore:

10 rad/s² ≈ 1.59155 rev/s²

Gradian Based Units

CalculatorKits also includes:

grad/s²

and:

grad/min²

A gradian, also called a gon, divides a full revolution into 400 parts.

Therefore:

400 grad = 360°

and:

1 grad = 0.9°

NIST gives the relationship between gon and degree as 0.9 degree per gon.

For example:

1 grad/s² = 0.9 °/s²

Because:

1 °/s² ≈ 0.0174533 rad/s²

we get:

1 grad/s² ≈ 0.015708 rad/s²

Gradian units can be useful in surveying and other applications involving angular measurements.

RPM Based Units

Two particularly useful units in the CalculatorKits converter are:

RPM/s

and:

RPM/min

RPM means revolutions per minute.

These units describe how quickly a rotational speed measured in RPM changes with time.

RPM/s

RPM/s means:

revolutions per minute per second

For example:

100 RPM/s

means that rotational speed increases by 100 RPM every second.

Because:

1 RPM = 2π/60 rad/s

we get:

1 RPM/s ≈ 0.10472 rad/s²

Therefore:

100 RPM/s ≈ 10.472 rad/s²

RPM/min

RPM/min means:

revolutions per minute per minute

This is equivalent dimensionally to rev/min².

The conversion is:

1 RPM/min = 1 rev/min²

Since:

1 rev/min² = 2π/3600 rad/s²

we get:

1 RPM/min ≈ 0.00174533 rad/s²

The distinction between RPM/s and RPM/min is important.

RPM/s describes a change in RPM every second.

RPM/min describes a change in RPM every minute.

They are not numerically interchangeable.

Mixed Time Units in the Calculator

Your converter also includes three less common mixed time units:

rev/min·s

rev/h·s

rev/h·min

These units are useful when rotational acceleration is expressed using different time intervals in the denominator.

rev/min·s

This represents:

revolution per minute per second

It has the same physical unit as RPM/s.

Therefore:

1 rev/min·s = 1 RPM/s

and:

1 rev/min·s ≈ 0.10472 rad/s²

rev/h·s

This represents:

revolution per hour per second

Since:

1 hour = 3600 seconds

we get:

1 rev/h·s = 2π/3600 rad/s²

Therefore:

1 rev/h·s ≈ 0.00174533 rad/s²

rev/h·min

This represents:

revolution per hour per minute

Since one hour is 60 minutes:

1 rev/h·min = 1/60 rev/min²

Therefore:

1 rev/h·min ≈ 0.0000290888 rad/s²

These units are less common in basic physics, but including them makes the CalculatorKits converter useful for more specialized rotational calculations.

Angular Acceleration Conversion Reference

Here are some of the most useful conversions involving the common SI based units.

From	To	Conversion
1 rad/s²	°/s²	57.2958
1 rad/s²	rev/s²	0.159155
1 rad/s²	RPM/s	9.5493
1 rev/s²	rad/s²	6.28319
1 °/s²	rad/s²	0.0174533
1 RPM/s	rad/s²	0.10472
1 rev/min²	rad/s²	0.00174533
1 RPM/min	rad/s²	0.00174533
1 rev/min·s	rad/s²	0.10472
1 rev/h·s	rad/s²	0.00174533
1 rev/h·min	rad/s²	0.0000290888
1 grad/s²	rad/s²	0.015708

The time based conversions for hours, days, and years follow the corresponding time definition used by the converter. This is particularly relevant for year based units because the exact length assigned to a year should be consistent throughout a conversion system.

Common Angular Acceleration Conversions

Convert 1 rad/s² to °/s²

Use:

°/s² = rad/s² × 180/π

Therefore:

1 rad/s² ≈ 57.2958 °/s²

Convert 1 rad/s² to rev/s²

Use:

rev/s² = rad/s² ÷ 2π

Therefore:

1 rad/s² ≈ 0.159155 rev/s²

Convert 100 RPM/s to rad/s²

Use:

rad/s² = RPM/s × 2π/60

Therefore:

100 × 2π/60 = 10.472 rad/s²

Answer:

100 RPM/s ≈ 10.472 rad/s²

Convert 1000 RPM/min to rad/s²

Because RPM/min is equivalent to rev/min²:

1000 × 2π/3600

≈ 1.74533 rad/s²

Therefore:

1000 RPM/min ≈ 1.74533 rad/s²

Angular Acceleration and Angular Velocity

Angular acceleration and angular velocity are closely connected.

Angular velocity tells you how quickly an object is rotating.

Angular acceleration tells you how quickly that angular velocity changes.

For constant angular acceleration:

ω = ω₀ + αt

Suppose a motor starts from rest and accelerates at:

20 rad/s²

for:

5 seconds

Then:

ω = 0 + (20 × 5)

ω = 100 rad/s

The motor reaches an angular velocity of 100 rad/s after five seconds.

This relationship is useful when analyzing motor startup, machine acceleration, braking, and controlled rotational motion.

Angular Acceleration and Torque

Angular acceleration is also connected to torque and moment of inertia.

The rotational form of Newton’s second law is:

τ = Iα

where:

τ = torque

I = moment of inertia

α = angular acceleration

Rearranging gives:

α = τ/I

For example, suppose a rotating system experiences 20 N·m of torque and has a moment of inertia of 4 kg·m².

Then:

α = 20/4

α = 5 rad/s²

The angular acceleration is therefore 5 rad/s².

BIPM identifies newton metre as the SI unit for torque and rad/s² as the SI unit for angular acceleration.

Angular Acceleration and Rotational Kinematics

Angular acceleration is used in several rotational motion equations.

For constant angular acceleration:

ω = ω₀ + αt

Angular displacement can be calculated with:

θ = θ₀ + ω₀t + ½αt²

Another useful equation is:

ω² = ω₀² + 2α(θ − θ₀)

These equations are rotational equivalents of familiar linear kinematics formulas.

For example, a shaft starts from rest and has an angular acceleration of 4 rad/s² for 5 seconds.

Its angular displacement is:

θ = ½ × 4 × 5²

θ = 50 rad

The shaft therefore rotates through 50 radians during that period.

When using these equations, keeping the angular units consistent is essential.

Angular Acceleration in Real World Applications

Electric Motors

Electric motors frequently have rotational speed specifications in RPM. During startup, engineers may need to know how quickly that RPM increases.

For example, a motor that increases from 1000 RPM to 4000 RPM in 2 seconds has an average acceleration of:

(4000 − 1000) ÷ 2 = 1500 RPM/s

Converting this to rad/s² gives:

1500 × 0.1047198 ≈ 157.08 rad/s²

Vehicle Engines

Engine speed is usually displayed in RPM. The rate at which engine speed changes can therefore be expressed using RPM/s or RPM/min.

These values can be useful when analyzing acceleration, engine response, drivetrain behavior, or rotational control.

Robotics

Robotic joints need controlled angular acceleration so they can move quickly while maintaining stability and minimizing mechanical stress.

Flywheels

Flywheels may experience large changes in rotational speed during startup and braking. Angular acceleration is important when analyzing these changes.

Turbines and Rotating Machinery

Turbines, compressors, pumps, generators, and machine tools all involve rotating components. Engineers may encounter different angular acceleration units depending on the equipment documentation or measurement system.

Gyroscopes

Gyroscopes use rotational motion for stabilization, navigation, and sensing. Changes in rotational speed can be analyzed using angular acceleration.

Angular Acceleration vs Angular Velocity

These two quantities are often confused.

Quantity	What it measures	SI unit
Angular velocity	Rate of angular motion	rad/s
Angular acceleration	Rate of change of angular velocity	rad/s²

For example, a motor rotating steadily at 100 rad/s has:

Angular velocity = 100 rad/s

Angular acceleration = 0 rad/s²

If the motor begins speeding up, its angular acceleration becomes nonzero.

If it begins slowing down, angular acceleration may be negative depending on the selected positive rotation direction.

Common Mistakes When Converting Angular Acceleration

1. Reversing the revolution and radian factor

Remember:

1 revolution = 2π radians

Therefore:

1 rev/s² = 6.28319 rad/s²

while:

1 rad/s² = 0.159155 rev/s²

The conversion factor changes depending on the direction of conversion.

2. Confusing RPM with RPM/s

RPM measures rotational speed.

RPM/s measures the rate at which rotational speed changes.

They are different physical quantities.

3. Confusing RPM/s with RPM/min

These units have different time denominators.

RPM/s means RPM changes every second.

RPM/min means RPM changes every minute.

The numerical conversion is therefore different.

4. Treating rev/min² and rev/min·s as identical

They are not identical.

rev/min² means:

rev/(min × min)

while:

rev/min·s means:

rev/(min × s)

Because one minute is 60 seconds, these units differ by a factor of 60.

5. Forgetting that the time unit is squared

Changing from seconds to minutes in an angular acceleration unit requires the time conversion factor to be squared.

For example:

1 min = 60 s

therefore:

1 min² = 3600 s²

This is why:

1 rad/min² = 1/3600 rad/s²

6. Mixing angular velocity and angular acceleration

A value such as 500 RPM is an angular velocity.

A value such as 500 RPM/s is an angular acceleration.

Always check the complete unit before performing a calculation.

7. Rounding too early

If several conversions are performed in sequence, rounding each intermediate value can create unnecessary error.

For engineering calculations, retain additional precision until the final result.

Why Use the CalculatorKits Angular Acceleration Converter?

The CalculatorKits Angular Acceleration Converter is useful when you need to work with different rotational acceleration conventions without manually calculating every conversion.

Its unit selection covers:

1. 5 radian based units: rad/s², rad/min², rad/h², rad/d², rad/year².
2. 5 degree based units: °/s², °/min², °/h², °/d², °/year².
3. 5 revolution based units: rev/s², rev/min², rev/h², rev/d², rev/year².
4. 3 mixed time units: rev/min·s, rev/h·s, rev/h·min.
5. 2 gradian based units: grad/s² and grad/min².
6. 2 RPM based units: RPM/s and RPM/min.

That gives you 22 angular acceleration units in one converter.

The tool is particularly useful when you receive a technical value in an unfamiliar rotational unit and need to quickly express it in rad/s² or another unit required by your calculation.

For high precision engineering, safety critical machinery, or regulated measurements, the converted value should still be checked against the applicable technical specification or measurement procedure.

Angular Acceleration Converter FAQs

What is the SI unit of angular acceleration?

The SI unit is radian per second squared (rad/s²). BIPM identifies rad/s² as the SI derived unit for angular acceleration.

How many degrees per second squared are in 1 rad/s²?

1 rad/s² ≈ 57.2958 °/s²

How many revolutions per second squared are in 1 rad/s²?

1 rad/s² ≈ 0.159155 rev/s²

How many rad/s² are in 1 rev/s²?

1 rev/s² ≈ 6.28319 rad/s²

How do I convert RPM/s to rad/s²?

Use:

rad/s² = RPM/s × 2π/60

Therefore:

1 RPM/s ≈ 0.10472 rad/s²

How do I convert rad/s² to RPM/s?

Use:

RPM/s = rad/s² × 60/(2π)

Therefore:

1 rad/s² ≈ 9.5493 RPM/s

Is RPM/min the same as rev/min²?

Yes. RPM means revolutions per minute, so RPM/min represents a change in revolutions per minute per minute. It is equivalent to rev/min².

Is RPM/s the same as rev/min·s?

Yes, mathematically they represent the same combination of time units:

RPM/s = rev/(min·s)

The notation is simply different.

What is the difference between rev/min² and rev/min·s?

They are different units.

rev/min² = rev/(min × min)

rev/min·s = rev/(min × s)

Since one minute equals 60 seconds, they differ by a factor of 60.

What is 1 rad/min² in rad/s²?

Because one minute equals 60 seconds:

1 rad/min² = 1/3600 rad/s²

Therefore:

1 rad/min² ≈ 0.000277778 rad/s²

What is 1 rev/min² in rad/s²?

Use:

1 rev/min² = 2π/3600 rad/s²

Therefore:

1 rev/min² ≈ 0.00174533 rad/s²

What is the difference between angular velocity and angular acceleration?

Angular velocity measures how quickly an object rotates.

Angular acceleration measures how quickly that angular velocity changes.

Angular velocity uses rad/s, while angular acceleration uses rad/s².

Can angular acceleration be negative?

Yes. A negative angular acceleration indicates a change in angular velocity in the negative direction according to the selected coordinate convention.

What is the relationship between torque and angular acceleration?

The basic rotational relationship is:

τ = Iα

where τ is torque, I is moment of inertia, and α is angular acceleration.

Therefore:

α = τ/I

How many units does the CalculatorKits Angular Acceleration Converter support?

The converter shown on CalculatorKits supports 22 angular acceleration units, covering radians, degrees, revolutions, gradians, RPM, and different combinations of seconds, minutes, hours, days, and years.

Is the Angular Acceleration Converter useful for RPM calculations?

Yes. The converter includes both RPM/s and RPM/min, along with several revolution based units, making it useful for rotational speed change calculations.

Related CalculatorKits Tools

If you are working with rotational motion, these four CalculatorKits tools are especially useful:

1. Angular Velocity Converter
   Convert angular velocity between rad/s, RPM, degrees per second, revolutions per second, and other rotational units.
2. Acceleration Converter
   Convert linear acceleration between m/s², ft/s², g, Gal, and other acceleration units.
3. Torque Converter
   Convert torque values between commonly used metric and imperial units.
4. Moment of Inertia Calculator
   Calculate rotational inertia for systems involving torque and angular acceleration.

Conclusion

Angular acceleration measures how quickly angular velocity changes over time. It is fundamental to rotational mechanics and is used in electric motors, engines, turbines, flywheels, robotics, gyroscopes, vehicle systems, and industrial machinery.

The SI unit is rad/s², but real world calculations can use many different combinations of angular and time units.

The CalculatorKits Angular Acceleration Converter includes 22 units:

rad/s², rad/min², rad/h², rad/d², rad/year²

°/s², °/min², °/h², °/d², °/year²

rev/s², rev/min², rev/h², rev/d², rev/year²

rev/min·s, rev/h·s, rev/h·min

grad/s², grad/min²

RPM/s, RPM/min

The most useful relationships to remember are:

1 rev = 2π rad

1 rad/s² ≈ 57.2958 °/s²

1 rad/s² ≈ 0.159155 rev/s²

1 rev/s² ≈ 6.28319 rad/s²

1 RPM/s ≈ 0.10472 rad/s²

1 rad/s² ≈ 9.5493 RPM/s

1 rev/min² = 1 RPM/min ≈ 0.00174533 rad/s²

When you need to convert between these units quickly, the CalculatorKits Angular Acceleration Converter provides all 22 units in one place.

For educational work, engineering calculations, and unit checking, this can save considerable time compared with performing each conversion manually. For safety critical or certified engineering applications, always verify the final result against the applicable technical specification or measurement standard.

References

1. NIST, SI Units and Derived Units
2. NIST, Guide to the SI
3. BIPM, International System of Units
4. ISO, Quantities and Units

• Written and reviewed by the CalculatorKits Editorial Team
• Last Updated: September 10, 2026