MachineCalcs

Gear Pitch Line Velocity Calculator

Calculate gear pitch-line velocity from pitch diameter and RPM, or derive pitch diameter from module, diametral pitch or circular pitch and tooth count. Includes transmitted power when torque is entered.

Gears 8 inputs 7 results

Calculator

Choose whether to enter pitch diameter directly or derive it from tooth size and count.
Operating pitch diameter of the gear.
mm
Rotational speed of the checked gear.
rpm
Optional running torque used only for transmitted power. Leave at 0 when unknown.
N·m

Results

Default result
Edit inputs
Pitch-line velocity(v)
5.0265m/s
Pass

Low to moderate pitch-line speed for a first-pass geometry screen.

v = pi*d*n/60.

Also computed

Pitch-line speed per minute(V)301.59m/min

Pitch diameter used(d)80mm

Pitch circumference(pi*d)251.33mm

Revolutions per second(n/60)20rev/s

Transmitted power(P)Pass12.566kW

Power from entered running torque and RPM.

Applied torque used(T)100N·m

Method notes 3 notes
  • Pitch-line velocity uses the operating pitch diameter: v = pi x d x n / 60 with d in metres and n in rpm.
  • When module, diametral pitch or circular pitch is entered, pitch diameter is derived from d = m*z, m = 25.4/DP or d = z*p_c/pi.
  • This is a speed and power screen only. It does not rate tooth bending, pitting, lubrication, dynamic factor, balance, noise or bearing reactions.

Gear pitch-line velocity is the linear speed at the pitch circle: v = pi*d*n/60, where d is operating pitch diameter in metres and n is gear RPM. If pitch diameter is not known, this calculator derives it from d = m*z, m = 25.4/DP or d = z*p_c/pi, then reports pitch-line speed, pitch circumference and optional transmitted power from P = T*omega.

Continue workflow

All Gears

How to use this calculator

  1. Choose the diameter basis. Enter pitch diameter directly, or derive it from module, diametral pitch or circular pitch and tooth count.
  2. Enter gear speed. Use the RPM of the checked gear, not necessarily the motor RPM if a prior reduction exists.
  3. Enter torque when known. Torque is optional; it is only used to calculate transmitted power from P = T x omega.
  4. Read speed and power. Use pitch-line velocity for lubrication and dynamic checks, and transmitted power for the next mesh-force or shaft workflow.

How it works

Gear pitch-line velocity is the circumference at the pitch diameter times revolutions per second: v = pi x d x n / 60 Use d in metres and n in RPM to get metres per second. The same result is also shown as metres per minute or SFM.

If the pitch diameter is not known, the calculator derives it from tooth size: d = m x z m = 25.4 / DP d = z x p_c / pi Optional transmitted power uses the entered running torque: P = T x 2 x pi x n / 60

Use this as the quick speed screen before deeper checks. For tooth loads, move to the gear mesh force calculator. For tooth size conversions, use the gear pitch calculator or pitch diameter calculator. For shaft and bearing sizing, continue with overhung load and bearing load.

Worked example

Verified against the live calculator

A gear with an 80 mm pitch diameter running at 1200 rpm has pitch-line velocity: pi x 0.08 x 1200 / 60 = 5.03 m/s. The pitch circumference is 251.3 mm, or 0.251 m per revolution. With 100 N*m of running torque, transmitted power is 100 x 2 x pi x 1200 / 60 / 1000 = 12.57 kW.

Reference data

This calculator uses geometry and speed inputs only. It does not select a gear material, AGMA/ISO rating factor, lubrication method or allowable pitch-line speed.

Pitch-line velocity inputs.
Input Role
Pitch diameter Direct operating pitch diameter, or d = m*z from module and teeth.
Diametral pitch Converted with m = 25.4 / DP before d = m*z.
Circular pitch Converted with d = z*p_c/pi.
Gear RPM Rotational speed at the checked gear.
Applied torque Optional input for transmitted power only.

Source: Formula geometry from pitch diameter, module, diametral pitch, circular pitch and RPM.

Frequently asked questions

What is gear pitch-line velocity?

Pitch-line velocity is the linear speed at the gear pitch circle. It is the speed a point on the pitch diameter travels, so it depends on pitch diameter and RPM.

How do you calculate pitch-line velocity?

Use v = pi x d x n / 60, where d is pitch diameter in metres and n is gear speed in rpm. The calculator also shows the same speed as m/min or SFM.

Can I calculate it from module or diametral pitch?

Yes. Enter module and teeth, diametral pitch and teeth, or circular pitch and teeth. The calculator derives pitch diameter first, then calculates pitch-line velocity.

Is pitch-line velocity the same as transmitted power?

No. Pitch-line velocity is speed. Transmitted power also needs torque: P = T x omega. This calculator reports power only when you enter a running torque.

Does this rate the gear for strength or lubrication?

No. It is a speed and power screen only. Tooth bending, pitting, dynamic factor, lubrication, noise, balance and bearing loads need separate gear-rating and drivetrain checks.

Method & assumptions

  • Uses the operating pitch diameter of the checked gear; outside diameter is not interchangeable.
  • Assumes constant running RPM and steady torque for the optional power output.
  • Does not apply service factor, gear efficiency, dynamic factor, face-load distribution or mesh friction.
  • Does not rate tooth bending strength, pitting/contact stress, lubrication, balance, noise, thermal limits or bearings.
Embed this calculator on your site free

Paste this where you want the calculator to appear. It stays in sync — same formulas, metric & imperial, light/dark — and a small credit link helps people find more tools.

Open widget

Live preview