# The Relationship Between Watts and Speed on a Stationary Bike

If you are a cycling enthusiast, you might have wondered how to measure your performance on a stationary bike. One of the most common metrics used by cyclists is wattage, which indicates how much power you produce with your legs. But what does wattage really mean on a stationary bike, and how does it relate to your speed?

In this blog post, we will explain the concept of wattage, the factors that affect it,

## What is wattage?

Wattage is a measure of the power you produce with your legs to get your bike going (and, preferably, going fast). You can think of it as the ultimate measure of your biking skills: the more power you produce, the better cyclist you are.

The cycling power is measured in watts. One watt corresponds to one joule of energy produced every second. The wattage displayed on your stationary bike shows the average amount of energy transferred in a standard period, such as one minute or one hour.

The wattage calculation on a stationary bike is based on the power output of the rider. This power output is measured by a device called a power meter. The power meter measures the torque and cadence of the pedals and calculates the power output by multiplying the torque by the cadence. The resulting value is the power output in watts.

## How does wattage relate to speed?

On a road bike, wattage measures the energy transferred to move the bike forward. Since a stationary bike doesn’t move, an adjustment is required in order to get a meaningful measure.

Stationary bikes have frictive elements that resist the movement of the pedal. These take the place of the combined weight of the bike and rider so that overcoming their resistance releases energy.

The relationship between the wattage and speed of a bike is not a straightforward one because the power output can be impacted by the resistance of the bike and the rider’s body. However, it is generally true that a higher wattage output will result in a higher speed, although there may be other factors that can come into play as well.

Now, I’m no mathematician. But, with a little bit of Internet research, I came across the formula expressing the relationship between wattage and speed when riding a bike.

Thanks to the bright minds of Bogna Szyk and Łucja Zaborowska, who came up with the formula below. All the succeeding information about this topic is from the Cycling Wattage Calculator (omnicalculator.com).

where:

P is your power in watts;
Fg is the resisting force due to gravity;
Fr is the rolling resistance force;
Fa is the aerodynamic drag;
v is your speed in meters per second; and
loss is the percentage loss in power.

As you can see from the formula, wattage increases with speed but also with other factors such as slope, gear, and wind resistance. We will look at each of these factors in more detail in the next section.

## What factors affect wattage for outdoor rides?

Four main factors affect wattage when riding a bike: gravity, rolling resistance, aerodynamic drag, and power losses.

### Gravity

If you’re cycling uphill, you need to overcome the force of gravity. Naturally, if you’re going downhill, gravity will actually help you, making you accelerate without any additional effort. The force of gravity can be calculated as follows:

Fg​=g×sin(arctan(slope)) × (M+m)

where:

Fg is the force of gravity in newtons;
g is the gravitational acceleration (9.81 m/s^2);
slope is the angle of inclination of the road in degrees;
M is your mass in kilograms; and
m – Weight of your bicycle and any extra gear, also in kg.

As the formula shows, gravity depends on your weight and the steepness of the hill. The steeper the hill, the more power you need to climb it. Conversely, the steeper the descent, the more power you gain from gravity.

### Rolling resistance

Rolling resistance is the force that opposes the motion of a wheel on a surface. It depends on several factors, such as the type and pressure of the tires, the quality and lubrication of the bearings, and the roughness and texture of the pavement.

Rolling resistance can be calculated as follows:

where:

Fr is the rolling resistance force in newtons;
Crr the rolling resistant coefficient

The rolling resistance coefficient varies depending on the type and pressure of the tires and the surface condition. For example, knobby tires have higher rolling resistance than slick tires, and soft or uneven surfaces have higher rolling resistance than hard or smooth surfaces. You can find the details here.

### Aerodynamic drag

Aerodynamic drag is the force that opposes the motion of an object through air. It depends on several factors, such as the shape and size of the object, the density and viscosity of the air, and the speed and direction of the wind.

Aerodynamic drag can be calculated as follows:

Fa​=0.5×Cd​×A×ρ×(v+w)2

where:

Fa is the aerodynamic drag force in newtons;
Cd is the Drag coefficient;
A is the frontal area of the object in square meters;
ρ is the density of the air in kilograms per cubic meter; and
v is the relative speed of the object and the air in meters per second.

As you can see from the formula, aerodynamic drag depends on the frontal area and the coefficient of drag of the object, the density of the air, and the square of the speed. This means that aerodynamic drag increases with your size and shape, the air pressure and temperature, and the speed. The wind also affects aerodynamic drag, depending on its direction and intensity. For example, a headwind will increase aerodynamic drag, while a tailwind will decrease it.

### Power losses

Power losses are the inefficiencies that occur in the transmission of power from your legs to the bike. They include friction in the chain, gears, pedals, and crankset, as well as heat dissipation and sound production. Power losses are usually expressed as a percentage of the total power produced.

You don’t have to worry about computing all these numbers yourself. Just go to Cycling Wattage Calculator (omnicalculator.com) and input the values; it will compute the answer for you.

I found another calculator here that shows the relationship between your cycling power (wattage) and speed for outdoor rides.

## How can you use wattage to improve your cycling skills?

Wattage is a useful metric to monitor and improve your cycling performance. By tracking your wattage, you can:

• Measure your progress over time. You can compare your wattage at different stages of your training and see how much you have improved.
• Set realistic goals and challenges. You can use wattage to determine your optimal intensity and duration for different types of workouts, such as intervals, endurance, or recovery.