E-bike Hill Climb Power Calculator

How this e-bike hill power calculator works

This calculator estimates how much power an e-bike must deliver to maintain a steady speed while riding uphill. It combines three main forces that oppose your motion: gravity pulling you back down the slope, rolling resistance from the tires, and aerodynamic drag from the air. From these, it computes the mechanical power required at the wheel and then estimates the electrical power drawn from the battery by accounting for motor efficiency.

Use it to answer practical questions such as:

• Can my current motor handle a particular hill at my usual speed?
• How much slower should I ride to stay within my motor’s continuous rating?
• How does adding cargo or a passenger change the required power?

Forces involved in climbing a hill

When you climb a slope at constant speed, the motor must supply enough power to balance three main components:

1. Gravitational component – lifting the combined mass of rider and bike against gravity.
2. Rolling resistance – energy lost as the tires flex and roll over the surface.
3. Aerodynamic drag – pushing air out of the way as you move forward.

The total mechanical power at the wheel can be written as the sum of these three contributions:

Each term is computed from basic physics:

• Gravity: proportional to total mass, slope steepness, and speed.
• Rolling resistance: roughly proportional to weight and speed, and depends on tire type and surface.
• Aerodynamic drag: grows very quickly with speed (with the cube of velocity in the power equation).

Core formulas used by the calculator

The calculator uses SI units internally: mass in kilograms (kg), speed in meters per second (m/s), distances in meters (m), and power in watts (W). Your speed input in km/h is converted to m/s inside the script.

Grade and slope angle

Road grade is usually expressed as a percentage:

grade (%) = 100 × (vertical rise / horizontal run)

If we call the grade G, then the slope angle θ satisfies:

From this, the script derives an expression for sin θ that uses the grade directly:

Mechanical power at the wheel

Let:

• m = total mass (bike + rider + cargo) in kg
• g = acceleration due to gravity ≈ 9.81 m/s²
• v = speed in m/s
• C_rr = rolling resistance coefficient
• ρ = air density (assumed 1.225 kg/m³)
• CdA = aerodynamic drag area in m²

Then the calculator approximates total mechanical power as:

Electrical power from the battery

Real motors and drive systems are not perfectly efficient. If we call the overall efficiency η (a value between 0 and 1), the electrical power drawn from the battery is approximated as:

The calculator reports both mechanical power at the wheel and estimated electrical power draw so that you can compare them to your e-bike’s rated motor power and battery capabilities.

How to interpret your results

After you enter your inputs and run the calculation, you will see required power in watts. Here are some ways to interpret those numbers in the context of common e-bike setups:

• Compare to motor ratings: Many consumer e-bikes have continuous motor ratings in the range of 250–750 W, with higher short-term peak power. If the required mechanical power is close to or above your motor’s continuous rating, the bike may still climb the hill, but it may need to slow down or may run hotter on long climbs.
• Allow for a safety margin: It is sensible to leave some headroom between the estimated required power and your motor’s continuous rating to account for wind, imperfect efficiency, and variations in grade.
• Check electrical power against your system: The electrical power estimate tells you roughly how hard the battery and controller are being asked to work. High sustained electrical power for long periods can accelerate heating and wear.

If the calculated required power is higher than what your system can realistically provide, you can usually make the climb easier by reducing speed, reducing total mass, or choosing a route with a lower average grade.

Worked example: typical commuter climb

Suppose a rider wants to know whether their e-bike can sustain 15 km/h on a 5% hill. They enter the following values:

• Total mass: 100 kg (bike + rider + gear)
• Grade: 5%
• Speed: 15 km/h
• Rolling resistance coefficient: 0.005 (typical for good pavement with city tires)
• Aerodynamic CdA: 0.6 m² (upright rider)
• Motor efficiency: 0.85

Internally, the calculator converts 15 km/h to about 4.17 m/s and computes the slope angle corresponding to a 5% grade. It then calculates the gravitational, rolling, and aerodynamic power components and sums them to get the required mechanical power. For this set of values, the total mechanical power comes out to a few hundred watts, and the electrical power is higher once efficiency is taken into account.

If the resulting electrical power is comfortably below the bike’s continuous motor rating, the rider can expect to hold roughly that speed on the given hill under calm, normal conditions. If the calculated power is near or above the motor’s rating, they may need to climb more slowly or use more of their own pedaling effort to avoid overheating.

How grade, speed, and mass affect required power

The same bike and rider can face very different power demands depending on the slope and speed. The table below illustrates relative effects using a single example bike. These numbers are illustrative and will differ from what the calculator displays for your exact inputs, but the trends are representative.

Increasing any of the three key inputs – grade, speed, or total mass – will raise the power needed. Grade mainly affects the gravitational term, speed has a strong effect on both gravitational and aerodynamic terms, and mass affects both gravity and rolling resistance.

Assumptions and limitations

The results from this calculator are estimates based on an idealized physical model. Real-world riding conditions are more complex. Keep the following assumptions and limitations in mind when planning a hill climb:

• Constant speed and grade: The model assumes that you ride at a steady speed on a uniform slope. In reality, grades can vary along a climb and speed may fluctuate.
• No wind or drafting: Air is assumed to be still. Headwinds increase aerodynamic drag and required power, while tailwinds reduce it. Drafting behind another rider or vehicle can also lower drag significantly.
• Standard air density: Air density is fixed at a typical sea-level value. High altitude, very cold, or very hot conditions will change air density and therefore drag.
• Rolling resistance simplification: The rolling resistance coefficient is treated as a single constant. In practice it depends on tire pressure, tire construction, surface roughness, and temperature.
• Single efficiency value: Motor and drivetrain efficiency are represented by one overall number. Actual efficiency varies with motor speed, torque, controller behavior, and gear selection.
• No thermal limits: The calculator does not model motor or controller heating or thermal protection. A system may be able to deliver a certain power briefly, but not continuously on a long climb.
• Bike and rider posture: Aerodynamic CdA is sensitive to riding position, clothing, and accessories (baskets, panniers, child seats). Small posture changes can meaningfully change drag at higher speeds.
• Human pedaling contribution: The calculation focuses on total required power and the portion supplied electrically. Your own pedaling effort can reduce how hard the motor and battery need to work, but is not modeled separately here.

Because of these factors, treat the output as a planning tool rather than a guarantee. It can help you compare scenarios, choose appropriate speeds, and understand how different choices affect power demand, but it cannot predict every detail of real-world performance.

Using the calculator for route and equipment planning

You can apply this model in several practical ways:

• Checking a new commute: Estimate the steepest section of your route and use the calculator to see how much power is needed at your desired speed. Compare this with your e-bike’s motor rating.
• Comparing cargo loads: Increase the total mass field to reflect extra cargo or a child seat to see how much more power and battery draw to expect on hills.
• Exploring speed trade-offs: Try lower and higher target speeds on the same grade to see how quickly required power rises. This can guide you toward an efficient climbing speed that balances time and battery use.
• Evaluating upgrades: Experiment with lower rolling resistance values or lower CdA to see how better tires or a more aerodynamic position could help on your terrain.

By understanding the physics behind hill climbing and how different variables contribute to required power, you can make better decisions about routes, equipment, and riding style, and reduce the risk of overloading your e-bike system on demanding climbs.