Belt Frequency Calculator for natural frequency, reverse tension or linear mass, open-pulley free span, engineering units, wave speed, and harmonics.
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- Surface Speed (SFM) Calculator
Belt Frequency Formula
The calculator models the free belt span as a vibrating string. Pluck the belt, measure the frequency, and you can solve for tension. Or work the other direction: pick a target tension and calculate the frequency you should tune to.
- f = belt vibration frequency, Hz
- T = belt tension (static strand tension), N
- m = belt mass per unit length, kg/m
- L = free belt span between pulley tangent points, m
- C = pulley center distance, m
- D = large pulley pitch diameter, m
- d = small pulley pitch diameter, m
The Natural frequency solve option uses the first equation. Give it the belt mass per metre, the span, and the tension you want to set, and it returns the frequency a belt tension meter or phone app should read.
The Belt span tension solve option uses the second equation. Pluck the belt, enter the measured frequency, and it returns an idealized static tension estimate for the strand.
The Frequency from pulley geometry option derives the straight tangent span L for an open drive and calculates frequency. The Mass per length option reverses the same string model.
Reference Tables
The mass per metre of the belt is the input people usually have to look up. The values below are illustrative only and are not verified specifications for a particular belt. Use the complete belt mass per metre supplied by its manufacturer.
| Belt type / section | Mass per metre (kg/m) |
|---|---|
| Classical V-belt, Z / 10 | 0.06 |
| Classical V-belt, A / 13 | 0.11 |
| Classical V-belt, B / 17 | 0.19 |
| Classical V-belt, C / 22 | 0.34 |
| Narrow V-belt, SPA | 0.12 |
| Narrow V-belt, SPB | 0.20 |
| Narrow V-belt, SPC | 0.37 |
| Timing belt, HTD 8M, 20 mm wide | 0.10 |
| Timing belt, HTD 14M, 40 mm wide | 0.36 |
Frequency readings convert directly to and from cycles per minute. The table below covers the range a phone tachometer app will typically capture.
| Frequency (Hz) | Cycles / min | Period (ms) |
|---|---|---|
| 10 | 600 | 100 |
| 25 | 1500 | 40 |
| 50 | 3000 | 20 |
| 75 | 4500 | 13.3 |
| 100 | 6000 | 10 |
| 150 | 9000 | 6.67 |
Worked Examples and FAQ
Example 1: Find the target frequency. An SPB narrow V-belt drive needs 280 N of static tension. Belt mass is 0.20 kg/m and the free span is 0.72 m. Apply f = (1 / (2 × 0.72)) × √(280 / 0.20) = 0.694 × 37.42 = 25.98 Hz. This corresponds to about 26 Hz under the ideal model; use the manufacturer installation specification.
Example 2: Convert a meter reading to tension. Same belt, same span, and the meter reads 32 Hz. Apply T = 4 × 0.20 × 0.72² × 32² = 4 × 0.20 × 0.5184 × 1024 = 424.67 N. This exceeds the example target of 280 N under the ideal model; follow the manufacturer procedure and specification.
Why does the belt have to be plucked, not just measured at rest? The formula uses the natural frequency of the span. You excite that frequency by tapping or plucking the belt midway between the pulleys. A sound or vibration meter then captures the decaying tone.
Does this work on a running drive? No. Stop and isolate the drive before measuring, and follow the manufacturer safety procedure. Running vibrations are outside this stationary-span model.
Which span do you measure on a drive with an idler? Each span vibrates independently. Measure the span you intend to tension, and use that span length in the formula.
How accurate is the method? There is no universal accuracy percentage or minimum span. Belt stiffness can bias the estimate, especially on short spans. Use manufacturer span limits, specified belt mass and installation tension; follow its measurement and calibration procedure.
