The pulley calculator above answers the two questions that come up whenever a belt connects two shafts. Given both pulley diameters and the driver speed, it returns the speed of the driven shaft. Given a target driven speed instead, it returns the diameter the driven pulley has to be. Either way it also reports the drive ratio, the belt speed at the rim, the torque the driven shaft sees and the power passing through the drive.
Arb Digital builds free tools that answer one question properly rather than several loosely. This page deliberately does not compute belt length, because the site already has a belt length calculator that does it from the two diameters and the centre distance, and duplicating it here would only split the answer across two pages. Size the speed here, then take the diameters over there for the belt itself.
What This Pulley Calculator Does
A belt that does not slip carries the same linear speed at the rim of both pulleys. That single fact produces everything else. If the rim speeds match, then the product of diameter and rotational speed must match too, so a small pulley driving a large one turns the large one slowly, and a large pulley driving a small one spins it fast. The ratio of the two speeds is exactly the inverse of the ratio of the two diameters.
The tool works in both directions because both are real problems. Checking an existing drive means measuring what is fitted and predicting the output speed. Specifying a new one means starting from the speed the machine needs and working back to a sheave size you can actually buy, which is why the reverse mode exists and why it reports the required diameter in the same unit you entered.
Torque is included because it is the half of the trade that people forget. A drive that reduces speed multiplies torque by the same ratio, so the driven shaft, its bearings, its key and its coupling all see more torque than the motor produces. That matters more often than the speed does, because a shaft sized for motor torque can be undersized for the torque arriving after a large reduction. Related shaft questions are covered by the torque calculator and the polar moment of inertia calculator.
How to Use It
- Choose the direction. Solve for driven speed when the drive already exists; solve for driven diameter when you are selecting a sheave to hit a required speed.
- Enter pitch diameters, not outside diameters. The belt rides on the pitch line, and on a grooved V-belt sheave that sits below the rim. Using the outside diameter biases the ratio, and the error is worse on small sheaves.
- Use the loaded driver speed. An induction motor slips under load, so a nameplate 1,800 RPM motor typically turns nearer 1,750. Entering the synchronous speed overstates every downstream figure by that few per cent.
- Enter the driver torque if you want the force side. The torque and power outputs need it. Leave it at zero and the speed and ratio results still work.
- Check the belt speed before you commit. It is the number that decides whether a drive is comfortable or marginal, and it is the one most easily overlooked.
The Formula: How Pulley Speed and Ratio Are Calculated
The core relationship is the equality of rim speeds. The linear speed at a radius is the radius multiplied by the angular velocity, a result set out in OpenStax University Physics Volume 1, section 10.3 on relating angular and translational quantities. Setting the two rim speeds equal gives N1D1 = N2D2, so the driven speed is N2 = N1D1/D2 and the diameter needed for a target speed is D2 = N1D1/N2.
Belt speed itself is the circumference multiplied by the rotational rate, v = πDN/60 with D in metres and N in revolutions per minute, giving metres per second. The drive ratio quoted in the results is D2/D1, which is greater than one for a reduction and less than one for an overdrive. Torque scales with that ratio and with efficiency: T2 = T1(D2/D1)η. Power is torque multiplied by angular velocity, P = Tω = 2πTN/60. The unit conventions used throughout — newton metres for torque, watts for power, metres per second for belt speed — follow NIST Special Publication 811, the guide to the use of the SI.
Work the defaults. A 100 mm driver at 1,750 RPM against a 250 mm driven pulley gives 1,750 × 100 ÷ 250 = 700 RPM. The drive ratio is 250/100 = 2.5, a reduction. Belt speed is π × 0.1 × 1,750 ÷ 60 = 9.16 m/s. With 10 N·m at the driver and no losses, the driven shaft sees 10 × 2.5 = 25 N·m, and the power through the drive is 2π × 10 × 1,750 ÷ 60 = 1,833 W, or 1.83 kW. Check it from the output side: 2π × 25 × 700 ÷ 60 = 1,833 W, the same figure, which is the arithmetic confirming that the belt moved the power without changing it.
Why Belt Speed Decides More Than the Ratio Does
Two drives with an identical ratio can behave completely differently, and belt speed is usually why. A drive running at a few metres per second is placid. The same ratio built from much larger sheaves at the same shaft speeds runs the belt several times faster, and the consequences arrive together: centrifugal tension rises with the square of the speed and pulls the belt away from the groove, which reduces the grip it was meant to add; the belt flexes around each pulley more times per minute, and flex cycles are what eventually fatigue it; and any imbalance in the sheaves is excited harder.
The opposite failure is a drive with too little belt speed, where power at low speed means high tension for the same transmitted power. Tension is what loads the shafts and bearings, and a slow, heavily tensioned drive can wear out bearings that a faster, lighter one would never trouble. This is the reason belt drives are usually placed on the fast shaft of a machine rather than the slow one, which is a design habit worth understanding rather than copying blindly.
Small sheaves cause a separate problem. Bending a belt around a tight radius strains its outer fibres, and every manufacturer publishes a minimum sheave diameter for each belt section for exactly that reason. This page does not publish those minimums, because they belong to a specific belt cross-section from a specific maker and a generic table would be a guess dressed as data. Take the diameter from the belt manufacturer's catalogue for the section you are actually using.
Where the Ideal Ratio Stops Being the Real One
The calculation above assumes the belt does not slip and does not stretch. Real flat and V-belt drives creep slightly: the belt is under more tension on the tight side than the slack side, so it is fractionally longer entering one pulley than leaving the other, and the driven shaft turns marginally slower than the ratio predicts. On a properly tensioned V-belt drive this creep is small, but it is a systematic loss rather than a random one, and it grows as tension falls.
Toothed synchronous belts remove this entirely, because their teeth engage the pulley grooves and the ratio becomes exactly the tooth-count ratio with no creep at all. If your drive has a timing belt, use tooth counts rather than measured diameters and the answer is exact. If it has a chain, the same applies with sprocket teeth.
The efficiency field handles the power side of the same story. Setting it below 100 per cent reduces the reported output torque, which is the honest way to model the loss, because the speed is set by geometry while the torque is what the losses eat into. What efficiency to use is not a question this page can answer for you: it depends on belt type, tension, sheave size and alignment, and the number belongs to the drive manufacturer's data sheet.
How This Differs From the Adjacent Drive Tools
The boundary in one sentence: this page converts between pulley diameters and shaft speeds in both directions and reports the torque that comes with the change, while the belt length calculator takes those same diameters plus a centre distance and returns the belt itself, its wrap angle and its free span.
The gear ratio calculator handles multi-stage gear and sprocket chains where several reductions compound, which a single belt pair does not do. The engine rpm calculator works the vehicle drivetrain chain from tyre size and final drive. For the rotational quantities behind all of them, the angular velocity calculator converts between RPM, radians per second and rim speed, and the mechanical advantage calculator covers the force-multiplying case including block-and-tackle pulley systems, which despite the shared word are a different machine entirely.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Measuring the outside diameter — the belt rides on the pitch line, which sits inside the flange on a V-belt sheave, and the resulting ratio error is largest on the smallest pulleys.
- Using the nameplate synchronous speed — an induction motor slips under load, so the real driver speed is a few per cent lower and every result scales with it.
- Forgetting that the driven shaft sees more torque — a reduction multiplies torque by the ratio, and the shaft, key and bearings downstream have to carry it.
- Mixing units between the two diameters — the ratio is dimensionless only if both diameters are in the same unit, and a millimetre against an inch is a factor of 25.4 error.
- Assuming a timing belt behaves like a V-belt — a synchronous belt has no creep and its ratio is the tooth-count ratio exactly, so measured diameters are the wrong input for it.
Related Free Tools From Arb Digital
For the belt itself, use the belt length calculator. For compounded reductions across gears or sprockets, use the gear ratio calculator, and for a vehicle drivetrain the engine rpm calculator. The angular velocity calculator and the torque calculator cover the underlying rotational quantities, the mechanical advantage calculator covers lifting pulley blocks, and the polar moment of inertia calculator covers whether a shaft can carry the torque. Rescale values with the power converter or the length converter, and browse the full free online tools hub for everything else.
Frequently Asked Questions
The one attached to the power source, normally the motor or engine shaft. The driven pulley is on the machine being turned. Swapping them in the inputs inverts the ratio and turns a reduction into an overdrive, so the labels matter.
The pitch diameter, where the belt actually rides. On a V-belt sheave that sits below the outer rim because the belt wedges into the groove, and using the outside diameter makes the calculated ratio slightly wrong in a way that gets worse as the sheaves get smaller.
Because belt length also needs the centre distance between the shafts, which this page does not ask for, and because the site already has a belt length calculator that does the job properly including wrap angle and free span. Size the speed here and take the diameters there.
No. It trades speed against torque and passes the power through, minus losses. Reducing speed by a factor of two raises torque by about the same factor, and the product stays close to the input power. Any tool suggesting otherwise has made an arithmetic error.
Because flat and V-belts creep. The belt is under greater tension on the tight side than the slack side, so it stretches unequally around the loop and the driven shaft lags the ideal ratio a little. Toothed synchronous belts and chains do not creep, and their ratio is the exact tooth-count ratio.
That depends on the belt construction and the sheave sizes, and it is specified by the belt manufacturer rather than by any general rule. What is generally true is that centrifugal tension grows with the square of belt speed and works against the wedging grip a V-belt relies on, so fast drives need attention to tension and balance.
Yes, for the speed and ratio, provided you use sprocket tooth counts in place of the diameters. A chain does not creep, so the ratio is exact, and the tooth counts are a more reliable input than a measured pitch circle.
Whatever the drive manufacturer's data gives for your belt type, tension and sheave sizes. This page does not publish a figure because efficiency depends on all of those and a generic number would be a guess. Leaving it at 100 per cent gives the ideal ratio, which is the right starting point for the speed side.
This tool is provided for educational and estimating use only. It is not a mechanical design specification, and it does not address belt selection, minimum sheave diameters, service factors, shaft and bearing loading, guarding or alignment. Power transmission equipment should be selected and installed by a qualified engineer using the manufacturer's rating data.
