Belt, pulley and gear ratio calculator
Enter pulley diameters or gear tooth counts and the input speed; for up to four stages see output speed, total ratio, torque, belt speed and belt length. For vibration analysis the shaft, gear mesh and belt frequencies are listed; in reverse mode you find the tooth pairs closest to a wanted speed.
Stages
The calculation runs in your browser; the values you enter are not sent anywhere.
- Output speed
- 483.33 rpm
- Total ratio (driven / driver)
- 3
- Torque factor (ratio × efficiency)
- 2.88
- Input torque
- 49.4 N·m
- Output torque
- 142.26 N·m
- Output power
- 7.2 kW
Stage by stage
| Stage | Input speed | Output speed | Ratio | Belt speed (m/s) | Belt length (mm) |
|---|---|---|---|---|---|
| 1 | 1,450 | 483.3 | 3 | 7.59 | 1,845 |
Frequencies for vibration analysis
Look for these frequencies and their multiples in the spectrum. Sidebands spaced at shaft speed on either side of the gear mesh frequency can indicate wear or eccentricity.
| Stage | Input shaft (Hz) | Output shaft (Hz) | Belt rotation (Hz) |
|---|---|---|---|
| 1 | 24.17 | 8.06 | 4.12 |
Assumptions and simplifications
- No slip: belt slip and gear backlash are ignored. On real V and flat belts slip can lower output speed by a few percent; toothed belts do not slip in normal operation.
- Power is taken as constant; output power = input power × the product of stage efficiencies, and torque is calculated from that power at the output speed.
- Belt length is given by an approximate formula for an open belt (L ≈ 2C + π(D₁ + D₂)/2 + (D₂ − D₁)²/4C); it is not rounded to standard belt lengths, and the belt manufacturer's calculation applies.
- For gear stages, external gears are assumed, so each stage reverses the direction of rotation; this does not hold for internal gears and planetary arrangements.
i = driven / driver · n₂ = n₁ / i · T = 9550·P/n (N·m; kW, rpm) · v = π·D₁·n₁/60000 (m/s) · gear mesh = Z·n/60 (Hz) · L ≈ 2C + π(D₁+D₂)/2 + (D₂−D₁)²/4C
The result rests on ideal kinematics and a simple efficiency assumption; the real speed varies with slip, load and supply frequency. For belt selection, power transmission and gear strength use the manufacturer's catalogue calculation.
Let's plan how to look for these frequencies in your vibration measurements and catch wear in your drive train before it fails.
Request a conversation01
How to use it
A
Choose the drive type (pulley or gear), then enter the input speed and the driver and driven size of each stage (up to four stages).
B
Read the output speed, the total ratio, the torque and the belt speed; see the frequency table for vibration analysis.
C
Switch to reverse mode to find the ratio needed for a wanted output speed and the closest tooth pairs in a tooth count range.
02
Ratio, speed and torque
In a pulley or gear pair the ratio is the driven element divided by the driver. If the ratio is greater than 1 the output slows down and torque rises. With power constant (apart from losses) speed and torque are inversely proportional: divide the speed by three and the torque rises roughly threefold.
In a multi-stage drive the ratios of the stages multiply; losses add up as the efficiency of each stage multiplies. That is why output power falls as the number of stages grows.
03
Belt speed and belt length
Belt speed is found as v = π · D · n / 60000 (D in mm, n in rpm). This speed must stay below what the belt type allows; the limit is in the belt manufacturer's catalogue.
If you enter the centre distance, the tool gives the approximate length of an open belt and the belt's rotation frequency. That frequency can correspond to a peak in the vibration spectrum when the belt is damaged.
04
Frequencies for vibration analysis
The gear mesh frequency is the tooth count times the shaft speed (Hz). In the spectrum this frequency and its multiples are among the first places to look when monitoring gear health; sidebands spaced at shaft speed on either side can be a sign of wear or eccentricity.
The same shaft frequencies are also the starting point for unbalance and misalignment: unbalance usually shows at shaft speed, misalignment often at twice shaft speed. The tool lists frequencies; interpretation takes measurement and experience.
FAQ
- How do I read a ratio: what does 3:1 mean?
- The driven element is three times the size of the driver (diameter or tooth count), the output speed is a third of the input and the torque is roughly three times. In the tool the ratio is given as driven / driver.
- Can I enter tooth counts instead of pulley diameters?
- Yes; use tooth counts for gears and toothed-belt pulleys. For flat and V-belt pulleys enter diameters; belt speed and length are calculated only with diameter input.
- Why is the output speed a little lower than what I measure?
- The tool does not account for slip. On V and flat belts, slip under load lowers the speed somewhat; the motor's actual speed can also differ from the nameplate value with load and supply frequency.
- Why does reverse mode give several tooth pairs?
- Many tooth pairs can give the same ratio (20:100, 21:105 and so on). The tool ranks by percentage error; a small total tooth count generally means a more compact drive. Teeth without a common factor spread wear more evenly, but that choice is the designer's.
- How do I look for the gear mesh frequency in vibration data?
- Look for the frequency in the table and its multiples in the velocity spectrum. The measurement resolution must be sufficient; remember that if the speed varies, so does the frequency. A rise in amplitude or the appearance of sidebands can point to gear wear but is not a diagnosis on its own.
Let's catch drive train faults early
Let's plan how to follow gear and belt frequencies in your vibration data and turn wear into a warning before failure.