Calculate belt frequency, tension, or span for open-belt drives from mass per metre, span, pulley diameters, and tension in Hz or N.
- All Physics Calculators
- Belt Speed Calculator
- Belt Length Calculator (2 pulley system)
- 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 = (1 / 2L) * sqrt(T / m)
T = 4 * m * L^2 * f^2
L = sqrt(C^2 - ((D - d) / 2)^2)
- 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 Frequency tab solves 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 Tension tab solves the second equation. Pluck the belt, enter the measured frequency, and it returns the actual tension in the strand.
The Span tab solves for L on an open belt drive when pulley diameters differ. Use that L value in either of the other tabs.
Reference Tables
The mass per metre of the belt is the input people usually have to look up. The values below are typical and should be replaced with the manufacturer figure when you have it.
| 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 = 25.99 Hz. Tune the belt until a meter reads about 26 Hz.
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 = 424.7 N. The belt is over-tensioned and needs to be backed off.
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. Take the reading with the drive stopped. A running belt has running vibrations that mask the natural frequency.
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? For spans of 0.25 m or longer with a clean pluck and a quiet environment, results are usually within 5 percent of a force-deflection check. Short spans, very stiff belts, and heavily damped belts reduce accuracy.
