# Cycling Wattage Calculator

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:

**P**is your power,**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 type | slick tires | knobby tires |
---|---|---|

concrete | 0.0020 | 0.0025 |

asphalt | 0.0050 | 0.0063 |

gravel | 0.0060 | 0.0076 |

grass | 0.0070 | 0.0089 |

off-road | 0.0200 | 0.0253 |

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,**v**is your speed,**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":

position | Cd * 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 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.

You can check out this article on mechanical resistance of bikes for more information about the power losses.

## 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 type | 5 minutes | 20 minutes | 1 hour |
---|---|---|---|

recreational | 2.5 | 2.1 | 1.8 |

amateur | 3.7 | 3.3 | 3.0 |

professional | 7.0 | 6.1 | 6.0 |