lb
Bike and gear weight
lb
Speed
mph
Position
Tops
Gear
Tires
Slick
Chain
New, well-oiled
External conditions
Surface
Asphalt
Wind speed
mph
%
Elevation
ft
a.s.l.
Wattage
Power
W
Power-to-weight ratio
W/
lb

# Cycling Wattage Calculator

By Bogna Haponiuk

This cycling wattage calculator is a tool designed for all cycling passionates. With its help, you can explore the relationship between the power you produce and various parameters such as speed, biking position, hill slope, or pavement type. For example, you can find out how much power you can save when switching from knobby to slick tires.

Thanks to this cycling power calculator, you will finally be able to compare two cyclists with fundamentally different styles - for example, a road cyclist who never gets off his slick-tired bike, and an MTB-enthusiast who enjoys hardcore off-road adventures.

## What is the cycling wattage?

Cycling wattage is 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 can produce, the better cyclist you are.

The cycling power is measured in Watts. One Watt corresponds to one Joule of energy produced every second.

Our cycling wattage calculator is based on the model described in detail in the paper "What is slowing me down? Estimation of rolling resistances during cycling". It assumes that the power you produce is equal to the sum of resistances you need to overcome, multiplied by your speed. Additionally, we take power losses into consideration.

The cycling wattage formula that we use looks like this:

`P = (Fg + Fr + Fa) * v / (1 - loss)`

where:

• Fg is the resisting force due to gravity,
• Fr is the rolling resistance force,
• Fa is the aerodynamic drag,
• v is your speed in m/s,
• loss is the percentage loss in power.

In the next sections of this text, we will look at each component of this cycling power equation in more detail.

## Component 1: gravity

If you're cycling uphill, you need to overcome the force of gravity. Naturally, if you're going downhill, the gravity will actually help you, making you accelerate without any additional effort.

The force of gravity can be calculated as

`Fg = g * sin(arctan(slope)) * (M + m)`

where:

• Fg is the resisting force due to gravity,
• g is the gravitational acceleration, equal to 9.80655 m/s²,
• slope is the slope of the hill, expressed as a percentage (positive for going uphill and negative for going downhill),
• M is your weight in kg,
• m is the weight of your bicycle and any extra gear, also in kg.

## Component 2: rolling resistance

The next factor that will undoubtedly slow you down is the friction between your tires and the surface. The smoother the road and the slicker your tires, the less friction you will experience.

The formula for rolling resistance is

`Fr = g * cos(arctan(slope)) * (M + m) * Crr`

where:

• Fr is the rolling resistance,
• g is the gravitational acceleration, equal to 9.80655 m/s²,
• slope is the slope of the hill, expressed as a percentage (positive for going uphill and negative for going downhill),
• M is your weight in kg,
• m is the weight of your bicycle and any extra gear in kg,
• Crr is the rolling resistance coefficient.

The estimates for the rolling resistance coefficient Crr in our cycling wattage calculator are based on the findings of researchers from the University of Pretoria and the University of Reims Champagne Ardenne:

surface typeslick tiresknobby tires
concrete 0.0020 0.0025
asphalt 0.0050 0.0063
gravel 0.0060 0.0076
grass 0.0070 0.0089
sand 0.0300 0.0380

## Component 3: aerodynamic drag

The third component of the power equation is the aerodynamic drag. It's a force of air resistance. Unlike the previous two components, it's dependent on your speed raised to the second power - the faster you are, the higher the air resistance. It means that the faster you go, the more difficult it is to keep speeding up.

The aerodynamic drag can be calculated according to the formula below:

`Fa = 0.5 * Cd * A * ρ * (v + w)²`

where:

• Fa is the aerodynamic drag,
• Cd is the drag coefficient,
• A is your frontal area,
• ρ is the air density,
• w is the wind speed (positive for head wind and negative for tail wind).

It is common to estimate the value of Cd * A instead of determining each of these two separately. We are using the values suggested by Asker E. Jeukendrup in his book "High Performance Cycling":

positionCd * A
tops 0.408
hoods 0.324
drops 0.307
aerobars 0.2914

The positions are:

• Tops - the hands hold the top straight portion of the handlebars.
• Hoods - the hands grip the brake level hoods at the top of the curved portion of the handlebars.
• Drops - the hands hold lower down the curve on the dropped or curved section of the handlebars.
• Aerobars - the hands grip the extra handlebars on the front of the triathlon bike.

Additionally, our cycling wattage calculator estimates the air density on a given elevation above sea level (a.s.l.) according to the barometric formula:

`ρ = ρₒ * exp[(-g * Mₒ * h) / (R * Tₒ)]`

where:

• ρ is the air density,
• ρₒ is the air density at the sea level, equal to 1.225 kg/m³,
• g is the gravitational acceleration, equal to 9.80655 m/s²,
• Mₒ is the molar mass of Earth's air, equal to 0.0289644 kg/mol,
• h is the elevation above sea level,
• R is the universal gas constant for air, equal to 8.3144598 N·m/(mol·K),
• Tₒ is the standard temperature equal to 288.15 K.

After substituting the constants, this equation can be simplified to

`ρ = 1.225 * exp(-0.00011856 * h)`

## Component 4: cycling power losses

Not all of the power that you produce when cycling is transferred directly to the wheels. Some of it is lost either due to the resistance of the chain or of the derailleur pulleys.

Our cycling power calculator assumes a constant 1.5% loss on your pulleys. The losses on the chain are dependent on its condition:

• 3% for a new, well-oiled chain;
• 4% for a dry chain (for example, when the oil has been washed away by rain);
• 5% for a dry chain that is so old it became elongated.

## Interpreting my result

Now you know your cycling wattage - but what does that number mean, exactly? The table below provides with an overview of the power-to-weight ratio (power that can be produced per kilogram of body weight) compiled by Dr. Andrew Coggan, a renown exercise physiologist.

cyclist type5 minutes20 minutes1 hour
recreational 2.5 2.1 1.8
amateur 3.7 3.3 3.0
professional 7.0 6.1 6.0

For a cyclist, power is probably the most useful piece of data you can get. By knowing your power you can learn about your performance, health, and even the state of your body. From all of these values the most mainstream of them has to be calorie consumption.

Not only are calories a common way for people to measure the level of activity they performed, but it also helps you better plan your nutrition and provides a measure by which you can set goals, be them fat loss, performance improvement, or building muscle.

It is for this reason that we have added a small feature under "Advanced mode" that lets you estimate the calories you burnt on your ride. This is a very simple process since power and energy are related by a single value: elapsed time.

When we are talking about a human doing some work, we also need to take into account the inefficiencies of our bodies. Our bodies always burn more energy than they produce and that difference is what we call efficiency. Once we model these losses into our formula we arrive at:

`Calories = ((Power * Time) / 4.18 ) / 0.24`

Where `Power` refers to the average power you sustained for the `Time` of the activity, `4.18` is the conversion factor from Joules (SI unit) to calories, and `0.24` is the efficiency (24%) of an average human body when cycling.

Remember that this is an estimation that works better for steady-paced rides than it does, for example, for HITT training. This is because the efficiency of our bodies changes slightly with power output and effort level.

If you want a more detailed analysis of your calorie consumption on the bike and the fat-loss implications, please visit out calories burned while cycling calculator.

Bogna Haponiuk