Bike Speed Calculator

This bike speed calculator works out your speed based on power. If you tell it how many watts both legs are producing, as well as your weight, riding position, road conditions and wind conditions, then it will calculate what actual speed you can ride at.

It is also possible to do the calculation in reverse. Enter your desired speed and the tool will tell you how much power it would take to achieve that. These are the physical laws that govern every bike ride. The speed is determined by where the power produced exactly equals the resistance.

The factors that actually determine speed are:

There are four forces that resist the motion of a bike. Both legs have to work against all these forces at once, and the speed they're in balance is the constant ride speed.

Air resistance is the resistance caused by moving through air. It is small at low speeds, but increases dramatically with increasing speed. This is because it is proportional to the square of the relative velocity to the air. At normal speeds on level ground, air resistance accounts for most of the power consumption.

Rolling resistance is the resistance that occurs due to deformation of the tire when it is pressed against the road surface. As it changes only slightly with speed, it is particularly important at low speeds and on climbs.

Gravity is a result of the gradient. When going up hill it can easily overcome other resistances while when going down hill it creates speed and acts in the opposite direction.

The power loss in the drive system is equivalent to a few percent consumed by chain and bearings between pedal and road surface. A clean and lubricated drive makes it possible to recover most of this loss.

Formula:

The four forces are added together, multiplied by the speed to convert force into power and divided by the efficiency of the drive system. This is the power that must be delivered by both legs.

where P is the pedal power in watts, v is the speed relative to the ground, m is the total mass of rider and bike, g is 9.8067, θ is the road gradient angle, C_rr is the rolling resistance coefficient, C_dA is the aerodynamic drag area, ρ is the air density, V_w is the headwind speed, and L is the drivetrain loss fraction.

When the speed is known, power can be easily calculated by plugging values into the formula. It is more difficult to determine the speed when the power is known. This is because the resistance terms develop a cubic equation in V. Since no simple formula can be used, a calculation tool numerically solves the equation. The instantaneous value for speed is displayed as this numerical solution is performed by the system.

Example calculation:

A rider who weighs 70 kg rides a bike that weighs 8 kg, holds the lower part of the handlebar firmly and uses high-quality road racing tires. He maintains an output of 200 W on flat terrain at sea level in windless conditions.

This is about 33.7 km/h or 20.9 mph. If you take a more aerodynamic position the speed will exceed 35 km/h with the same power of 200 W. On a city bike with an upright riding position, the speed falls below 30 km/h. Nothing has changed except for the air that needs to be moved.

Aerodynamics and drag coefficient:

CdA is the drag area, which is the product of the drag coefficient and the projected area, and is measured in square meters. This is a critical factor for speed on flat ground, and depends almost entirely on body position. The lower the value, the higher the speed.

As drag increases in proportion to the square of speed, the effect of a lower position is greatest at higher speeds. This is why time triallists are so concerned with reducing their projected area by even a few centimetres; a leisurely commuter will barely notice the difference.

Rolling resistance and Crr

The Crr value is a resistance coefficient that indicates how strongly a tyre behaves when rolling on the road. Soft slick tyres have a low value on smooth asphalt tracks, while wider block tyres on gravel roads have a multiple times higher value.

Rolling resistance changes proportionally to weight and remains nearly constant at different speeds. So it represents an invisible cost that you pay all day long. It also explains why the choice of tires and tire pressure can affect how a bike feels to ride in ways that most riders don't expect.

Weight, incline and power-to-weight ratio

On flat terrain the weight has little effect on speed. When going uphill, however, weight becomes a decisive factor. The power required to overcome an incline is the product of total weight, gravitational acceleration and degree of incline. Therefore, when climbing steep hills it is not absolute performance but rather performance per kilogram that counts.

For this reason, the calculator also shows the power-to-weight ratio. If two riders are both riding at 250 watts of power, but one weighs 60kg and the other weighs 90kg, there will be a big difference in the time it takes to climb the hill. On flat ground, weight is not as important as air resistance, so their speeds would be nearly identical.

Air, Altitude, Wind

The thinner the air, the less resistance there is. As air density decreases with altitude, you can go faster in the mountains at the same power output than on the coast. A calculator uses a standard air model and estimates the density based on altitude. You can also enter values directly.

Wind affects the resistance. The air does not sense the speed relative to the ground but rather the relative speed to the air. Headwind is like a huge invisible mountain range. Tailwind helps. By entering a negative value for wind speed, you can simulate a tailwind that assists forward motion.

Calculating Power based on FTP and Pace

If you're doing strength training, then you can use the calculator with your FTP (Functional Threshold Power) instead of an estimated wattage. The FTP is the power that you can sustain for about one hour and at certain intensities you will use a fraction of it. This fraction is called the intensity factor.

An FTP of 0.70 is a comfortable steady state pace that can be sustained for hours. About 0.85 is the threshold range and would be appropriate for an hour long challenging ride. Above 0.95 you are in race pace which can only be sustained for short periods of time. By switching to FTP mode, setting an intensity factor, then adding a distance will convert this information into an estimated finish time.

This is a static model that simulates how a rider maintains power while climbing at a constant gradient. As real rides involve acceleration, cornering, gusts and constantly changing gradients the results should be considered as educated estimates rather than exact measurements.