Convert angular velocity between rad/s, RPM, Hz, RPS, deg/s, and rev/h with a direct target result, period check, and full unit table.
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Angular velocity converter Convert signed angular velocity between rad/s, RPM, RPS, Hz, degrees per second, and slower engineering time bases without changing the direction sign.
Common presets
1 RPM = 0.1047 rad/s
Frequency still needs the 2π step
1 Hz equals one cycle per second, which is the same as one revolution per second. Angular velocity in SI is measured in radians per second, so converting from Hz to rad/s multiplies the same rotation rate by 2π.
Negative values preserve direction
Negative angular velocity stays negative so you can keep reverse rotation, coastdown, or sign-sensitive control-loop values intact. This page translates units only and does not choose a clockwise or counterclockwise sign convention for you.
Angular speed is not surface speed
Angular velocity describes how fast something rotates. Tangential or rim speed also depends on radius, so wheels, pulleys, and disks still need a separate linear-speed calculation.
Result
6.2832 rad/s
60 RPM equals 6.2832 rad/s. The same rotation rate is 6.2832 rad/s, 60 RPM, and 1 Hz.
Selected target
6.2832 rad/s
Radians per second
6.2832 rad/s
Degrees per second
360 °/s
Revolutions per minute
60 RPM
Revolutions per second
1 RPS
Hertz
1 Hz
Period per revolution
1 s
Quick reference
1 Hz = 1 RPS = 60 RPM = 6.2832 rad/s = 360 °/s.
1 rad/s = 9.5493 RPM = 0.1592 Hz, which is why frequency-style and angular-speed values are related but not numerically identical.
1 Hz is the same physical rotation rate as 6.2832 rad/s after the cycles-to-radians conversion is applied.
Angular velocity converter: rad/s, RPM, Hz, and deg/s explained
An angular velocity converter rewrites the same rotational rate into the unit your controls, drawings, formulas, or instrumentation expect. This page also explains the main assumptions behind the angular velocity converter result, highlights the supporting figures shown by the calculator, and helps the reader use the estimate without overstating what a quick online tool can prove.
How angular velocity units connect
Angular velocity describes the rate of angular change over time. One revolution equals 2π radians and 360 degrees, so every supported unit is a scaled expression of the same underlying motion.
That is why 1 revolution per second equals 2π rad/s, 360 degrees per second, 60 RPM, 1 Hz, and 3,600 revolutions per hour. The motion does not change when the label changes; only the reporting convention changes.
In physics and controls work, radians per second is often the cleanest base unit because it drops directly into equations. In operator-facing settings, RPM or degrees per second may be easier to interpret. This converter keeps those representations aligned so you can move between formulas, machine settings, and measurement displays without re-deriving the same relationship each time.
ω = dθ / dt
Defines angular velocity as change in angle over change in time.
1 revolution = 2π rad = 360°
Links revolution-based and angle-based expressions of the same rotation.
1 Hz = 1 cycle/s = 1 revolution/s = 2π rad/s
Shows why frequency-style cycle counts and angular velocity are connected through the 2π radian relationship.
RPM = RPS × 60
Converts between per-second and per-minute revolution counts.
Why Hz and rad/s are related but not numerically identical
Hertz measures cycles per second. Angular velocity in SI uses radians per second. Those are not the same unit label, but they describe the same repeating rotation once you account for the fact that each full cycle contains 2π radians.
That is why 1 Hz equals about 6.2832 rad/s rather than 1 rad/s. A frequent mistake in spreadsheets and controls notes is to treat a frequency number as though it can drop straight into an angular-velocity formula without the 2π conversion. This converter makes that relationship explicit instead of hiding it.
The same distinction matters when comparing RPS and RPM. Revolutions per second and revolutions per minute describe the same kind of count, but their time bases differ by a factor of 60. Converting cleanly avoids mixing an intuitive machine-speed display with the SI form needed by an equation.
How to read the direct target result and period check
Many searches for this topic are not asking for a full physics solver; they are trying to convert one practical rotational-speed label into another. A motor note may say 1500 RPM, a controller may ask for rad/s, and a sensor stream may expose Hz. The direct target result is designed for that exact source-to-target lookup.
The full conversion sheet remains useful because it shows the same rate in every supported unit family. The selected target is the quickest answer, while the rad/s value acts as the SI audit trail behind the conversion. If the direct result looks surprising, compare the Hz, RPS, RPM, and rad/s rows before using the value downstream.
The period check answers a related timing question: how long one full revolution takes at the entered angular velocity. For example, 60 RPM is 1 revolution per second, so the period is 1 second. A negative angular velocity still has a positive period because duration is based on the magnitude of the rotation rate, while the sign continues to describe direction.
Target value = source value × source factor in rad/s ÷ target factor in rad/s
Converts the input through radians per second before expressing it in the selected target unit.
Period per revolution = 1 / |cycles per second|
Finds the positive time for one full revolution from the equivalent Hz or RPS value.
60 RPM × π / 30 = 6.2832 rad/s
Shows the common RPM to rad/s conversion used by motor-speed and rotational-dynamics workflows.
Worked examples: motors, scanners, and reverse rotation
Suppose a motor data sheet reports a shaft speed of 60 RPM. Dividing by 60 gives 1 revolution per second, which is also 1 Hz. Multiplying that by 2π gives about 6.2832 rad/s, and multiplying by 360 gives 360 degrees per second. Every one of those values describes the same steady rotation rate.
Now consider a scanner or gimbal interface that reports 180 degrees per second. That same motion is 0.5 revolutions per second, 30 RPM, and about 3.1416 rad/s. Degrees-per-second formats are intuitive for sweep motion, but the rad/s form is easier to use in rotational-physics equations.
Signed values matter when the direction itself carries meaning. A value of -30 RPM remains negative after conversion, becoming about -3.1416 rad/s and -0.5 Hz. This converter preserves the sign so reverse rotation, braking, or axis-direction information is not lost during the unit change.
For a higher-speed motor example, 1500 RPM is 25 revolutions per second, 25 Hz, and about 157.08 rad/s. That same shaft has a period of 0.04 seconds per revolution, which can be easier to compare with sampling, encoder, or strobe timing than the angular velocity alone.
Angular velocity is not tangential speed or period
Angular velocity tells you how fast something rotates about an axis. Tangential or rim speed also depends on radius, so two disks can share the same angular velocity while their edges move at very different linear speeds.
Period is different again. Period measures the time required for one full cycle, while angular velocity measures how quickly the angle changes. If you know frequency, period is the reciprocal, but angular velocity still needs the 2π relationship to move between cycles and radians.
Use this converter to keep the angular-rate translation clean first. Then apply radius, path length, or separate timing formulas if your next step is surface speed, travel distance, or motion duration.
What this converter does not solve
This page translates angular-rate units only. It does not calculate angular acceleration, torque, power, inertia, stopping time, or tangential speed.
It also does not choose your positive or negative rotation convention. A negative value stays negative, but the engineering meaning depends on how your project defines the axis direction.
Use the converter to standardize the unit label, then move to a dedicated rotational-dynamics, acceleration, or linear-speed calculation if you need a design or analysis answer rather than a clean equivalent rate.
Multiply RPM by 2π and divide by 60. The compact form is RPM × π / 30. For example, 60 RPM equals 60 × π / 30 = 2π rad/s, which is about 6.2832 rad/s. The converter uses that same relationship internally, then also shows the equivalent degrees per second, RPS, Hz, and period.
What is the difference between RPM and rad/s?
RPM counts full revolutions per minute. Rad/s measures angular change directly in radians per second. The values differ by both the 2π relationship between revolutions and radians and the 60-second relationship between minutes and seconds. That is why 60 RPM equals 1 RPS and about 6.2832 rad/s rather than 60 rad/s.
Is Hz the same as angular velocity?
Not exactly. Hz is cycles per second, while angular velocity in SI is radians per second. They describe the same repeating motion once you account for the fact that one full cycle contains 2π radians. So 1 Hz equals 1 revolution per second and about 6.2832 rad/s.
Can angular velocity be negative?
Yes. A negative value can represent reversed rotation direction, braking, or motion opposite to the positive axis used in your model. The converter preserves the sign, but it does not decide whether clockwise or counterclockwise should be treated as positive in your project.
Why does the converter show period per revolution?
Period is the time for one full revolution. It is not another angular-velocity unit, but it is a useful cross-check when a rotational speed must be compared with timing, sampling, encoder pulses, or strobe intervals. The period is calculated from the magnitude of the equivalent Hz or RPS value, so a negative rotation rate still produces a positive duration while the converted angular-velocity rows keep the direction sign.
Is angular velocity the same as surface speed or period?
No. Surface speed depends on radius as well as angular velocity, so two rotating objects can share the same rad/s but have different rim speeds. Period is different too: it measures the time per cycle. Frequency and period are reciprocals, while angular velocity connects to them through the 2π radian relationship.
Can I use angular velocity to find tangential speed?
Only if you also know the radius. Tangential speed uses v = rω, so the same angular velocity can create different rim speeds on different wheels, pulleys, disks, or arms. Use this converter first to put ω in a consistent angular unit such as rad/s, then use a separate radius-based calculation for surface speed.
