angular velocity Calculator
Quickly compute angular velocity, convert between rad/s, deg/s, and RPM, and relate angular speed to linear velocity using radius. Perfect for engineers and students.
Rad per second to rpm converter:
Calculate and compute values of rotating motion with this Angular Velocity Calculator: any of the following angular velocity ( ω ), frequency (f), period (T), or RPM can be inputted and the calculator will give the corresponding values of rad /s, deg /s and RPM, as well as other quantities like linear (tangential) speed v = ω r and period T = 1 / f and angular acceleration when time data is available. Perfect for rapid unit conversion and problems of rotational kinematics.
angular velocity to linear speed equation tool Formula:
The Angular Velocity Calculator calculates the rotational speed using standard units and connects the angular and linear movement. With any one of the usual types of inputs, angular velocity (ω), rotational speed (RPM), angular frequency, period (T), frequency (f), or linear velocity with radius, the tool switches and determines the rest. It accepts units of rad/s, deg/s, and rpm and does conversion calculations such as 2pi/s = 57.7, which is 2pi/f, and RPM = 57.7/f. With circular motion problems, it also calculates the linear (tangential) velocity as v = 0WR and is capable of calculating period or frequency given angular quantities. The calculator can be handy in work by mechanical engineers, robotics designers, physics students, and any other person who works with rotating systems, shafts, and motors or oscillatory phenomena.
⚡ Work & Installation Input to Output:
Input: provide any known variable(s): angular velocity (rad/s or deg/s), RPM, frequency (Hz), period (s), radius (m) and/or linear speed (m/s), plus optional time and final/initial ω for angular acceleration. Select desired output units.
Processing: validate numeric inputs, convert inputs to SI (rad/s), apply formulas (ω = 2πf, ω = θ/t, RPM = 60f, v = ω·r, α = Δω/Δt). If solving quadratically or multiple-step problems (e.g., given v and r → ω → RPM), perform chained conversions.
Output: display values in rad/s, deg/s, and RPM; show linear speed if radius provided; show period and frequency; include step-by-step conversions and a concise diagnostic (e.g., inconsistent data warnings). Offer copyable results and CSV export.
Testing and Final Adjustments
Check with special cases: rpm/rad/s conversions (e.g. 60 RPM/2pi rad/s), zero speed and very high speeds, radius conversions (r=0 or r=0.01). Check frequency/period inverses (f = 1/T). Check angular acceleration,yesa (positive with accelerating, negative with decelerating). Check unit pickers, formatting, and rounding (present sensible accuracy but retain full export accuracy). UX tests: numeric keypad on mobile, clear labels ( ω, f, T, RPM), available ARIA attributes, and missing/contradictory input error messages. Add example presets (motor at 1800 RPM, wheel radius 0.3 m), add tooltip math hints. Complete with calculator, calculator meta tags, and schema.
Frequently Asked Questions - angular velocity Calculator:
What is angular velocity?
Angular velocity (ω) measures rotational speed — the rate of change of angle with time, usually in radians per second.
How do I convert RPM to rad/s?
Use ω (rad/s) = RPM × 2π / 60.
How do I get linear speed from angular velocity?
Linear (tangential) speed v = ω × r, where r is radius.
What is the relation between frequency and angular velocity?
ω = 2π × f, where f is frequency in hertz (cycles per second).
How do I find period from frequency?
Period T = 1 / f.
Can this calculator handle degrees per second?
Yes — it converts between rad/s and deg/s (1 rad/s ≈ 57.2958 deg/s).
What is angular acceleration?
Angular acceleration (α) is the rate of change of angular velocity: α = Δω / Δt.
Is RPM the same as angular velocity?
RPM (revolutions per minute) measures rotational speed but must be converted to rad/s to get angular velocity.
Can I use this for motors and wheels?
Yes — useful for motors, gears, wheels, turbines, and any rotating machinery when you need conversions or linear speed from rotation.
Does this calculator account for direction (sign) of ω?
Yes — it preserves sign for direction; positive/negative ω indicates rotation sense depending on your sign convention.
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