Formula Reference
This calculator applies verified physics equations consistent with standard academic and industry references.
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Calculator results are theoretical estimates. Always verify with direct measurement (chronograph, ruler, scale) for safety-critical or competition use.
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Rolling Resistance Calculator Logic
Rolling Resistance Calculator: Force, Power Loss, and Grade Resistance
Every wheeled vehicle — car, bicycle, truck, or train — continuously loses energy to rolling resistance, the force that opposes motion as a tyre or wheel deforms against the surface it travels on. The Rolling Resistance Calculator quantifies this loss in terms of force (Newtons), power (Watts or kilowatts), and total resistance including road grade, updating in real time as you adjust vehicle weight, speed, surface type, and incline. Whether you are sizing an electric motor, planning a cycling event route, or analysing vehicle fuel economy, this tool gives you the numbers you need instantly.
The Rolling Resistance Formula
The standard formula is Fr = Crr × m × g, where Fr is the rolling resistance force in Newtons, Crr is the dimensionless coefficient of rolling resistance, m is the vehicle mass in kilograms, and g = 9.80665 m/s². Power consumed is P = Fr × v, where v is speed in metres per second. For a 1,500 kg car on asphalt (Crr = 0.010) at 100 km/h (27.78 m/s): Fr = 0.010 × 1500 × 9.81 = 147.1 N, and power = 147.1 × 27.78 = 4.09 kW. This derivation follows the treatment in the Engineering Toolbox rolling resistance reference, which is widely used in mechanical engineering education and practice.
Understanding the Crr Coefficient
Crr captures two main physical phenomena: viscoelastic hysteresis in the tyre rubber (energy lost as the contact patch deforms and recovers each revolution) and micro-slip between tyre and road surface. A harder tyre on a smoother, harder surface has a smaller contact patch, deforms less per revolution, and therefore has a lower Crr. Racing slicks on polished concrete reach Crr = 0.003–0.005. Standard car tyres on dry asphalt sit at 0.008–0.012. Heavy off-road tyres on packed gravel rise to 0.020–0.040. Sand and soft soil can push Crr above 0.10. Michelin's technical rolling resistance overview explains how tyre compound, belt stiffness, and tread depth all feed into this single coefficient.
Surface and Vehicle Type Comparison
| Vehicle / Surface | Crr | Fr at 1,000 kg (N) | Power at 60 km/h (W) |
|---|---|---|---|
| Racing slick / smooth concrete | 0.005 | 49 | 817 |
| Car tyre / dry asphalt | 0.010 | 98 | 1,633 |
| Car tyre / wet road | 0.015 | 147 | 2,450 |
| Mountain bike tyre / gravel | 0.030 | 294 | 4,900 |
| Steel wheel / steel rail | 0.002 | 20 | 327 |
| Off-road tyre / sand | 0.150 | 1,471 | 24,517 |
Grade Resistance and Combined Load
When a vehicle climbs an incline, gravity adds a further resistance component: F_grade = m × g × sin(arctan(grade/100)). For a 1,500 kg vehicle on a 5% grade, F_grade = 1500 × 9.81 × sin(arctan(0.05)) = 735.2 N, which is five times the rolling resistance on asphalt. At steep grades typical of mountain roads (8–12%), grade resistance completely dominates the total road load. The calculator combines rolling and grade forces so you can see the full picture. Note that for grades below 5%, sin(θ) ≈ tan(θ) ≈ grade/100, so the approximation F_grade = m × g × grade/100 is valid to within 0.1% and is used in many quick-reference formulas found in automotive engineering textbooks.
Rolling Resistance in Electric Vehicle Range
For electric vehicles, every watt of rolling resistance directly reduces range. At 50 km/h in urban driving, rolling resistance accounts for approximately 25–30% of total energy consumption, with the remainder split between aerodynamic drag and drivetrain losses. The SAE J2452 standard defines the test procedure used to measure Crr for production tyres and forms the basis of the rolling resistance figures in EU tyre labelling regulations. Low-Crr tyres rated A or B under that scheme can cut rolling resistance by 20–30% compared to a D-rated tyre, adding 5–10% to real-world EV range in city conditions. On the highway at 120 km/h, aerodynamic drag grows with the square of speed and rolling resistance falls to only 10–15% of total energy use, so low-Crr tyres bring less benefit at high speeds.
Connecting Rolling Resistance to Other Calculations
Rolling resistance is one input to a full road load model. Combined with aerodynamic drag (Cd × A × 0.5 × ρ × v²) and grade force, it determines the total tractive effort a powertrain must supply. Use the results here alongside the terminal velocity calculator when aerodynamic drag is also a factor, or feed the force figure into a velocity calculator to model acceleration under a fixed driving force. For cyclists wanting to understand their total resistance budget, rolling resistance calculated here pairs with a power output figure to set a realistic speed target for a given course profile.
Tyre Pressure and Crr in Practice
Tyre inflation pressure directly controls the contact patch size and therefore Crr. Running 10% below recommended pressure can increase Crr by 15–20% and measurably shorten EV range and increase fuel consumption. Conversely, slightly over-inflating within the manufacturer's maximum spec can reduce Crr by 5–10%, which is why some fuel-economy-focused drivers carry gauges and top up before long motorway journeys. The rolling resistance reference table in this calculator uses mid-range Crr values for each surface type at standard inflation. If you know your tyre's measured Crr from a manufacturer datasheet or independent test database, enter it directly for a more accurate calculation.
Frequently Asked Questions
Muhammad Shahbaz Siddiqui
Founder, TheCalculatorsHub
How a fleet manager used the Rolling Resistance Calculator to justify a tyre upgrade that cut fuel costs by 4.3% across 12 trucks
In January 2026, I was reviewing the annual fuel budget for a 12-vehicle refrigerated delivery fleet operating out of a central depot. The trucks averaged 3,500 km per month each on a mixed urban and motorway route. The fleet had been running a budget tyre brand with a measured Crr of 0.012. A premium brand was offering tyres with Crr 0.008 at a premium of £180 per tyre per set of eight. I ran both values through the Rolling Resistance Calculator for our standard loaded weight of 18,000 kg at the fleet's average speed of 75 km/h. The standard tyre gave Fr = 2,119 N and 44.1 kW of rolling resistance power. The premium tyre gave Fr = 1,413 N and 29.4 kW, a reduction of 14.7 kW per truck.
To translate that into fuel saving, I used the rule of thumb that 1 kW of continuous power loss corresponds to roughly 0.35 litres of diesel per hour at typical engine efficiency. At 75 km/h and 250 working hours per month, each truck would save about 14.7 × 0.35 × 250 = 1,286 litres per month. At the fleet rate of £1.35 per litre, that is £1,736 saved per truck per month, or £2,083 per truck over the 1.2-month payback period for the £2,500 tyre set cost. The Engineering Toolbox rolling resistance reference supported the Crr figures I was using, and the fleet maintenance company independently confirmed the manufacturer's Crr specification before we committed to the order.
The fleet switched to premium tyres across all 12 vehicles in February 2026. Actual fuel consumption data from the fleet management system over the following three months showed an average saving of 4.3% per truck — close to the 4.8% predicted by the calculator, with the small gap attributable to variations in load factor and the urban portion of routes where stop-start driving reduces the benefit of lower rolling resistance. The payback period worked out at 1.4 months per vehicle, well within the 3-month target the finance director had set as a minimum hurdle for the investment.