The bicycle in numbers

Tools at a glance

The bicycle is a remarkably honest machine. Turn the pedals once and the rear wheel turns by the ratio of chainring teeth to sprocket teeth, carrying you forward by the wheel's circumference. Your legs feel heavy on a hill because gravity pulls you back by your weight times the sine of the gradient, and you get out of breath above 30 km/h because the power needed to overcome air resistance rises with the cube of speed. The calculators in this chapter work through that simple, honest physics for your own bike and body.

Under each calculator you'll find the formulas used, how to read the results, and how to put the numbers to use in practice. A result is a starting point, not the answer. The same pressure feels different depending on tire brand and rim internal width, and the same calorie estimate translates into different real burn depending on your body composition and efficiency. Use the numbers as a baseline and fine-tune by feel: that's the best way to use a calculator. Nothing you enter is sent anywhere; every calculation happens only in your browser.

Gear ratio & speed calculator

Gears are how a bicycle understands human legs. Our legs produce power most efficiently when pedaling at around 80–100 revolutions per minute, but the gradient and wind change constantly. To bridge that gap, the gears change the combination of front chainring and rear sprocket (cog), letting you ride at different speeds at the same pedaling rate (cadence). Enter your chainrings and cassette, wheel size and cadence in the calculator below, and it shows the speed for every gear combination in a single chart and table.

How it's calculated: from gear ratio to speed

Every calculation starts with the gear ratio: the chainring tooth count divided by the cog tooth count. A 50T chainring and a 25T cog give 2.0, meaning the rear wheel turns twice for each turn of the pedals. Multiply that by the wheel circumference and you get the distance the bike travels per pedal revolution: the development. A 700×28c tire has a circumference of about 2,136mm, so at a ratio of 2.0 you travel about 4.27m per revolution. Finally, multiply the development by the cadence and by 60 to get the distance per hour, and divide by 1,000 for speed in km/h.

Speed (km/h) = (chainring ÷ cog) × wheel circumference (m) × cadence (rpm) × 60 ÷ 1000

Gear inches is a long-standing measure in the English-speaking world: the gear ratio multiplied by the wheel diameter in inches. It's a holdover from the days of the high-wheeler (penny-farthing), before chain drive, when the diameter of the front wheel was the gear. A 30-inch gear feels like turning a 30-inch high-wheeler directly. Generally, 25 or under is a very easy gear that will get you up steep mountain roads, and over 100 is a big gear for fast flat riding or descents. In France and continental Europe, development (m) is used more than gear inches.

Reading the chart: overlap, gaps, cross-chaining

Where the rows for each chainring overlap on the chart is the overlap zone, where you can ride at similar speeds without shifting the front. A 2×11 drivetrain has 22 combinations in theory, but only about 13–15 gears actually differ from each other by more than 3%. The calculator's "effective gears" lines up the combinations, excluding cross-chaining, in order of gear ratio and counts only those that differ from the previous gear by 3% or more.

The spacing between dots on the same row is the step between shifts. With tight one-tooth steps like 11-12-13, your cadence changes by only 7–8% when you shift and your rhythm stays intact, but on a wide-range cassette such as 10-51, the steps at the big-cog end reach 15–20%, so a single shift on a climb feels dramatically different in your legs. Wide range and tight steps are a trade-off, and that's also why road bikes favor 2× drivetrains and MTBs 1×.

Cross-chaining means combining the big chainring with the biggest cogs, or the small chainring with the smallest cogs. The chain runs at an angle, increasing noise and friction, speeding up wear on the chain and teeth, and sometimes rubbing on the front derailleur cage. With two or more chainrings, the calculator marks the two cogs at each end as cross-chained. Most of these combinations can be replaced by a straighter one on the other chainring, so find the alternative gear on the chart. 1× drivetrains aren't marked, given how their chainline is designed, but spending a lot of time in the end gears still wears things faster.

Tire pressure calculator

Tire pressure is the most powerful tuning tool there is, costing nothing yet changing comfort, speed, grip and puncture resistance all at once. Because of the belief that "harder is faster", it used to be common to run 120psi in 23mm tires, but test results are now widely known showing that on real roads, inflating beyond the right level leaks energy through vibration and actually makes you slower. The calculator below estimates front and rear pressures as a starting point, based on body weight, tire width and surface.

How it's calculated: 15% tire drop

This calculator is based on the "15% tire drop" principle that American bicycle tech writer Frank Berto derived from measured data. The idea is that the pressure at which the tire compresses by about 15% of its height under the rider's weight strikes the balance between rolling resistance, comfort and rim protection. The load a tire supports is roughly pressure × contact area, and a wider tire has a larger contact area for the same drop, so it carries the same load at much lower pressure. The calculator splits the total weight (rider + bike + cargo) 46% front : 54% rear, the typical load distribution in a road or gravel position, then derives the base value with an approximation proportional to each wheel's load and inversely proportional to tire width to the power of about 1.55.

A few corrections are then applied. Tubeless is about 8% lower, since there are no "snakebite" punctures where the tube is pinched between rim and obstacle, and less internal friction. Rough roads are about 6% lower, gravel 14% and off-road 20%, so the tire swallows bumps, and on wet surfaces a further 5% is taken off to increase the contact area. These correction factors are averages based on the trends in pressure charts published by SRAM/Zipp, SILCA and tire manufacturers.

Using the result, and safety limits

The number you get is a starting point. Ride at the calculated value a few times; if road shocks jolt up through your hands and backside, drop 2–3psi at a time, and if the tire squirms in corners or you feel the rim bottoming out, add some. The ±5% range shown in the result box is where most people end up happy. Pressure gauges vary a lot, and it's common for two pump gauges to read 5psi or more apart, so sticking with one gauge consistently matters more than the number itself.

Calorie & power calculator

Cycling lets you burn a lot of energy over long periods while your weight rests on the saddle, keeping stress on your joints low. So how much did an hour's ride burn? This calculator takes your average speed, or the average power measured by a power meter, estimates the calories burned, and translates the number into familiar foods.

How it's calculated: why kJ and kcal are almost the same

The number a power meter shows is the mechanical work applied to the pedals. Ride for an hour at an average of 150W and you've done 150J/s × 3,600s = 540kJ of work. But the body uses only part of the chemical energy from food to turn the pedals and gives off the rest as heat. In cycling, this gross efficiency is generally known to be between 20% and 25%. At 24% efficiency, the energy actually used is 540 ÷ 0.24 = 2,250kJ, and since 1kcal = 4.184kJ, that's about 538kcal. Because 24% efficiency and the conversion factor of 4.184 almost cancel each other out, we get the handy rule that "in cycling, kJ ≈ kcal".

In average speed mode, a physics model (the same equation as the power simulator in the next section) first estimates the average power needed to hold that speed. It assumes a 10kg bike, a typical club rider's relaxed position (CdA 0.45) and ordinary asphalt (Crr 0.006), and adds 15% for the acceleration, braking, wind and surface changes of real roads. The "route type" equivalent grade expresses, as an average gradient, the share of energy spent climbing that you don't get back on the descent (lost to braking and to air resistance at higher speed). Real rides include waiting at lights, accelerating and braking, and wind, so the same average speed can differ from what a power meter shows; if you have a power meter, power mode is far more accurate.

The MET method, shown alongside for comparison, uses metabolic equivalent values from the US Compendium of Physical Activities. A fixed value for each speed band, such as 6.8 METs for 16–19 km/h, 8.0 METs for 19–22.5 km/h and 10.0 METs for 22.5–25.5 km/h, is multiplied by body weight (kg) and time (h). It's simple, but it can't account for gradient and wind, and the values jump in steps at the speed band boundaries. MET values also include resting metabolism and are based on lab measurements, so they tend to run a little high for typical club riding. It's more realistic to treat the two values as a lower and upper bound, with the actual burn usually somewhere in between.

Power required simulator

As a bike moves forward, the rider's legs battle three enemies: rolling resistance, from the tire deforming against the road; gravity, pulling you back on hills; and air resistance, which body and bike must push through. On top of that come drivetrain losses in the chain and bearings. This simulator shows how much power each resistance eats up as you change position, gradient, speed, weight and wind.

Formulas used

P = ( Crr·m·g·cosθ + m·g·sinθ + ½·ρ·CdA·v_a² ) · v ÷ η

Here m is the combined mass of rider and bike (kg), g is gravitational acceleration of 9.81m/s², θ is the slope angle (the arctangent of gradient % ÷ 100), v is ground speed (m/s), and v_a is airspeed including wind. ρ is air density, taken as 1.2kg/m³ at sea level and about 20℃, and η is drivetrain efficiency, set at 97%, a typical figure for a clean, well-maintained chain drive. In other words, it assumes that about 3% of the power that must reach the wheel is lost as heat in the chain and bearings.

CdA is the drag coefficient (Cd) multiplied by frontal area (A), and indicates how "wide" you look to the air. An upright city bike position is 0.5–0.6m², a road bike on the brake hoods about 0.32–0.40m², tucked low in the drops 0.28–0.32m², and a time trial position on aero bars about 0.20–0.25m². That's why pro riders spend hours refining their position in the wind tunnel. At 40 km/h on the flat, more than 80% of total power goes into air resistance, so cutting CdA by just 10% makes you noticeably faster for the same power.

What the numbers tell you

Move the sliders and a few laws emerge. First, on the flat, air resistance dominates. Double your speed and the air resistance force quadruples, while the power to overcome it rises eightfold. That's why going from 30 to 40 km/h takes far more extra power than going from 20 to 30 km/h. Second, on climbs, gravity dominates. Climbing a 7% grade at 12 km/h, air resistance is only a few tens of watts, but gravity demands hundreds. So on climbs, power-to-weight (W/kg) matters more than position, and a kilogram of bike weight feels more significant than on the flat.

Third, headwinds are harsher than you'd think. Riding at 25 km/h into a 15 km/h headwind is, as far as the air is concerned, the same as riding at 40 km/h. It's the same principle by which riders in a peloton save 20–30% or more of their power sheltering behind the rider in front (drafting). The "equivalent flat, no-wind speed" in the result box is the speed you'd reach if you poured your current power into flat, windless conditions, which is useful for getting a feel for how hard your effort on a climb or into a headwind is in flat-road terms.

Frame size & saddle height quick calculator

A bike that doesn't fit is uncomfortable no matter how expensive it is. If the frame is too big, the bars are too far away and your back and neck ache; too small and you feel cramped, knees nearly hitting the bars. The calculator below gives you a starting point for frame size and saddle height from just your height and inseam (inside leg length). Measuring and detailed fitting are covered in Chapter 04, Assembly & fit.

Saddle height uses the inseam × 0.883 formula popularized by Greg LeMond. This is the distance measured along the seat tube from the center of the crank axis (BB) to the top of the saddle. The 109% method, shown alongside, sets the distance from the pedal axle to the top of the saddle, with the pedal at its lowest point, to 109% of your inseam. Both formulas are rules of thumb based on 170–172.5mm cranks, so after setting your saddle from the result, check that your knee is bent about 25–35 degrees with the pedal at the bottom. When moving the saddle, change it a little at a time, no more than 5mm at once, to protect your joints.

Each manufacturer measures frame size differently, so the same "54" can be a different actual size. We show the traditional conversions, inseam × 0.665 (cm) for road and inseam (cm) × 0.226 (inches) for MTB, but these days comparing stack and reach is more accurate than seat tube length. If you're between two sizes, the usual advice is to go smaller if you're flexible and want an aggressive position, or bigger if you want comfort; a test ride in a shop is the surest way to know.

Chain length & replacement calculator

Most new chains come long, at 112–126 links, so they have to be cut to fit the bike. A chain that's too short can pull the rear derailleur taut when you combine the big chainring and big cog, damaging the hanger or frame; too long and it sags in small-gear combinations and can bounce or drop off. Chains also lengthen with use as the pins and rollers wear, and catching this "stretch" in time is the secret to making your cassette and chainrings last.

Chain length formula

L (inches) = 2 × C + F ÷ 4 + R ÷ 4 + 1

C is chainstay length (inches), F the largest chainring tooth count and R the largest cog tooth count. A chain's pitch (the distance between pins) is 1/2 inch, so each tooth needs 1/2 inch of chain to wrap around it. The chain wraps roughly halfway around both chainring and cog, so the wrapped length is (teeth ÷ 2) × 1/2 inch, or teeth ÷ 4 inches. The upper and lower runs joining front and back add up to twice the chainstay length, and the final inch is slack for wrapping around the rear derailleur pulleys. The result is rounded up to the nearest inch (= 2 links) to give an even number of links, because chains alternate inner and outer links, so a standard chain connector needs an even link count.

This formula is widely used in the repair trade, including by Park Tool, and on typical 2× road and gravel drivetrains it gives almost the same result as the practical "big-big plus two links" method. However, modern 1× MTB drivetrains with very large cogs such as 10-51T or 10-52T, and full-suspension frames (where the effective chainstay length grows as the suspension compresses), require the manufacturer's own method. SRAM Eagle, for example, says to wrap the chain around the big chainring and the largest cog (bypassing the derailleur) and add a set number of links at the overlap. Always treat the manufacturer's manual as the final word.

When to replace: 0.5% and 0.75%

A chain "stretching" isn't the metal getting longer; it's play building up between links as the pins and bushings wear. A stretched chain no longer sits precisely between the teeth and starts to eat them away. The usual recommendation is to replace the chain at 0.5% elongation for 11-speed and up, and 0.75% for 10-speed and below. Replace just the chain at that point and the cassette and chainrings can last through two or three chains. Leave it until nearly 1%, though, and the teeth wear too, so even a new chain will "skip" when you push hard, and the cassette has to be replaced as well. In distance terms, 3,000–8,000km is typical depending on care, but chains wear much faster if you often ride in the rain or on dirt, so get into the habit of checking with a chain checker every 1,000km.

"The right bike for you" quick quiz

Walk into a bike shop and road, gravel, hybrid, MTB, folding and electric bikes stand side by side. More important than which is best is the question "where, what for, and how much will I ride?" Answer five questions and we'll recommend the type of bike that best suits your lifestyle. You'll find the detailed characteristics of each type in Chapter 02, Bike types.

Unit conversion & average speed → distance

The cycling world is a jumble of units. Tire pressure mixes American psi and European bar, wheels are labeled in both inches (29-inch) and millimeters (700c, ETRTO 622), and overseas riding apps and race results often show miles. Type a number into any box of the converter below and the other side updates instantly. For reference, 1bar is about 14.5psi, 1 inch is exactly 25.4mm, and 1 mile is 1.609km.

The most common mistake in estimating distance is applying your bike computer's "average speed" to the total time from start to finish. Most devices calculate average speed using only moving time, excluding time stopped. So averaging 25 km/h over 100km doesn't mean you'll arrive in four hours. Add convenience store stops, waiting at lights and photo breaks, and total time easily grows by 20–30%. When planning a long ride, allow a generous share for stops, and check the sunset time and your last resupply point. Planning on 10–15% slower than your usual average speed is another trick for a safe plan, because fatigue and wind take a bigger toll in the later stages of a long route.

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