How to use this calculator
- Choose the diameter basis. Enter pitch diameter directly, or derive it from module, diametral pitch or circular pitch and tooth count.
- Enter gear speed. Use the RPM of the checked gear, not necessarily the motor RPM if a prior reduction exists.
- Enter torque when known. Torque is optional; it is only used to calculate transmitted power from P = T x omega.
- 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.
| 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.