Bike Gearing Calculator

Your gearing cannot change your climbing speed

This is the part most gear calculators get backwards. They ask you for a cadence and tell you the speed. On a sustained climb you do not choose the speed. Your power, your total weight and the gradient choose it, and the only thing left for the gearing to decide is how fast the cranks go round while that happens.

A rider putting out 200 watts at 80 kg on an 8% ramp goes 10.3 km/h. Fit a 34-tooth sprocket, fit a 25, fit anything you like: they still go 10.3 km/h, because the gear ratio is not a term in the balance between the rider and gravity. What changes is the cadence. On a 36 by 28 that speed is 63.4 rpm. On a 36 by 25 it is 56.6. On a 36 by 21 it is 47.6.

So the question worth asking is not which cassette is fastest. It is whether the easiest gear you own lets you pedal at a rate you can hold for the length of the climb, at the power you plan to ride.

What the cadence research actually says

Bernard and colleagues had nine well-trained triathletes ride 20 minutes at 60, 80 and 100 rpm at what they described as sprint-triathlon race intensity, above 80% of VO2max, then run 3000 m on a track. The run after the 60 rpm ride averaged 625.7 seconds, after 80 rpm 630.0, and after 100 rpm 637.7. Those differences were not statistically significant.

The same study did find differences either side of the finish time. Over the first 500 m of the run, stride rate and running velocity were significantly higher after the 80 and 100 rpm rides than after the 60 rpm ride, and the 60 rpm ride left the athletes running at a significantly higher fraction of their VO2max. So the run after the lower cadence cost more to produce, even though the clock did not show it.

Those measures disagree, and it is worth being plain about that rather than picking the flattering half. The only performance outcome, the 3 km time, came out fastest after the lowest cadence, non-significantly and in the wrong direction to lean on. The physiological and early-pace measures went the other way. Nothing in there picks a cadence, which is why the calculator does not offer one. Anywhere inside that range is yours to choose; what a gearing tool can settle is whether your bottom gear leaves you able to choose at all.

The mechanics underneath are not in dispute. A systematic review of cadence and neuromuscular function states that for a given power output, raising the pedalling cadence reduces the torque applied to the pedal, and lowering it raises the torque. Halve your cadence at the same power and the average pedal force doubles. Whether that extra force costs you anything over 90 km has not been settled.

So the failure worth catching before race day is not 78 rpm where you wanted 85. It is the athlete who discovers on the day that their bottom gear puts them at 44 rpm on a 12% wall, standing up, thirty kilometres from the run.

A worked example

Take an athlete at 80 kg all in, riding a 52/36 with an 11-28 on 700 by 25 tyres, planning to hold 200 watts on the steep sections of a hilly 70.3. At 8% the calculator gives 10.3 km/h and 63.4 rpm in the 36 by 28. That is inside the tested range, and on 172.5 mm cranks the average pedal force is about 175 N.

Now change one number. The same athlete carrying a bit more, at 95 kg all in and still holding 200 watts, is going 8.8 km/h. The 36 by 28 now gives 53.9 rpm, below the range anyone has tested, and the pedal force rises to about 205 N. To get back to 60 rpm they need a 32-tooth sprocket, which is a cassette swap their derailleur may well take.

The same logic runs the other way. Put the lighter athlete on a 12% pitch instead of 8% and the 36 by 28 gives 43.9 rpm at 7.2 km/h, with the average pedal force up at 252 N. No road cassette rescues that: 36 teeth, the largest a road rear derailleur normally takes, still only reaches 56.5 rpm, and dropping to the smallest common inner chainring does not get there either. A 40-tooth sprocket reaches 62.8 rpm, and buying one means a gravel or mountain derailleur as well as a cassette. On a pitch that steep the honest options are a wider-range drivetrain, more power, or riding it slowly.

How the speed is worked out

The speed comes from the steady-state power balance that Martin and colleagues validated for road cycling: the power you put into the pedals, less drivetrain losses, has to equal the power needed to lift you up the slope, plus rolling resistance, plus aerodynamic drag. Because those terms grow with speed at different rates, the equation is solved numerically rather than rearranged.

Two of the inputs are assumptions rather than measurements: the drag area and the rolling resistance coefficient. On a real climb neither matters much. At 200 watts, 80 kg and 8%, air resistance accounts for about 2% of the total resistive force and rolling resistance about 6%, while gravity does the other 92%. Raising the assumed drag area by a third moves the cadence by less than half an rpm. Below about 3% gradient the aerodynamic share grows enough to matter, and the calculator says so on screen when your gradient is that shallow.

Wheel circumference is the input most likely to be a little off. The estimate treats the tyre as round, so the outside diameter is the rim's bead seat diameter plus twice the tyre width. Real tyres sit differently on different rims, and a 1% error in circumference is a 1% error in cadence, about two thirds of an rpm at these numbers. Measure a rollout if you want that back.

Where this stops being reliable

It does not know whether the parts fit. Rear derailleurs have a maximum sprocket size and a total capacity, both specific to the model, and a recommendation here can easily exceed them. Check the manufacturer's specification, and expect a longer chain and possibly a different derailleur alongside a much bigger cassette.

It assumes you stay seated and steady. Standing changes the drag area and lets you push a bigger gear briefly; a punchy 400 m ramp is a different problem from a 40-minute pass, and this page models the second one.

It uses one gradient. Real climbs are not one gradient, and the number that catches people out is the steepest sustained section, not the average. Take the steepest part you will have to ride at a steady effort and use that.

It needs a power number, which is the one input not written on your bike, and the answer moves with it: 10 watts is worth about 3 rpm at the settings this page opens with. Without a power meter, estimate from a climb you have ridden at a steady effort. Kilograms times 9.8, times metres climbed, divided by seconds taken, gives the power that lifted you. Then add for rolling and air resistance: about a tenth on a pitch of 8% or steeper, a fifth at 5%, a third at 4%. Below about 4% the correction outgrows the part you can measure and the method stops being worth using. An estimate this rough can carry you across a band edge, so if the cadence lands within a few rpm of your target, read it as unresolved rather than as a verdict.

It says nothing about what power you should ride. The climbing power is the number you provide, and the calculator has no opinion about whether it suits your race, your fitness or your day.

Common questions

What cadence should I climb at?

The page does not tell you, because the evidence does not support a single number. In the triathlon study cited below, nine well-trained athletes rode 20 minutes at 60, 80 and 100 rpm before a 3000 m run. The run times did not differ significantly, and the fastest mean time actually followed the 60 rpm ride. The same study did find that the 60 rpm ride left them running at a higher fraction of VO2max, and running slower over the first 500 m, than 80 or 100 rpm did. Those measures point in opposite directions, so no cadence in that range has been shown to be the right one. What this calculator settles is whether your gearing lets you sit in that range at all.

Will a bigger cassette make me slower on the flat?

Only through the gaps between gears. Moving from an 11-28 to an 11-32 keeps the same 11-tooth top gear, so your maximum speed at a given cadence is unchanged, but the steps between sprockets get wider and it is harder to land exactly on the cadence you want on rolling terrain. The top gear figure on this page shows the speed at which your biggest gear runs out at 100 rpm, which is usually much faster than anyone pedals on a descent.

Why does my speed not change when I change the gearing?

Because gear ratio is not a term in the power equation. Your speed on a climb comes from the power you produce, your total weight, the gradient, and small contributions from rolling and air resistance. Changing gears changes how fast the cranks turn to deliver that power, not how much power you make. The exception is indirect: if a gear is so hard that you cannot hold the power at all, you slow down, and that is exactly the failure this page is looking for.

Should I use my FTP as the climbing power?

Almost certainly not. FTP is roughly what you can hold for an hour in a controlled test, and very few age-groupers ride a long-course climb at that number and still run well afterwards. Use the power you have actually held on long climbs in training. With no power meter, work backwards from a climb you have ridden at a steady effort: kilograms times 9.8, times metres climbed, divided by seconds taken, is the power that lifted you, then add about a tenth on a pitch of 8% or steeper and more than that on a shallower one. The optional FTP box here only reports what share of your FTP the figure you typed would be.

Will the cassette I need fit my bike?

This page cannot tell you. Rear derailleurs carry a published maximum sprocket size and a total capacity, and both vary by model and generation. A recommendation of a 34-tooth sprocket is a statement about cadence, not about compatibility. Check your derailleur's specification, and budget for a longer chain if you jump several sizes.

Sources

• Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics 1998;14:276-291. The power balance the speed solver implements. A free restatement of the same model, by different authors, is in Dahmen, Wolf and Saupe (2012), Applications of Mathematical Models of Road Cycling.
• Bernard T, Vercruyssen F, Grego F, Hausswirth C, Lepers R, Vallier J, Brisswalter J. Effect of cycling cadence on subsequent 3 km running performance in well trained triathletes. British Journal of Sports Medicine 2003;37(2):154-159. The 60, 80 and 100 rpm cycle-run trial that both band edges come from.
• Mater A, Clos P, Lepers R. Effect of cycling cadence on neuromuscular function. International Journal of Environmental Research and Public Health 2021;18(15):7912. The review behind the pedal-force statement.

Every figure the calculator produces follows from these sources and from the numbers you type. None of it is a measurement of you.