Library / Automotive and vehicle dynamics / VEH-10
Automotive and vehicle dynamics
Electric vehicle range estimate
Ideal driving distance from the usable battery energy and the average energy consumption per kilometre.
- Ref
- VEH-10
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- drange [km]
Eusable is the battery energy that can actually be used (kWh), which is less than the nameplate capacity, and ed is the average energy consumption of the vehicle in kWh per km, measured at the battery. The ratio gives the ideal range. Real range moves with speed, temperature, payload, terrain and heating or cooling loads, and recuperation during braking returns part of the energy.
Ideal driving distance from the usable battery energy and the average energy consumption per kilometre. Real range moves with speed, temperature, load and driving style.
Calculator
- Consumption in Wh/km180 Wh/km
- Energy per 100 km18 kWh
- Range in miles207.1 miles
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- 60 kWh of usable energy at 0.18 kWh/km (18 kWh per 100 km) gives 333.3 km. A 10 % rise in consumption, for instance from faster motorway driving where drag grows with speed squared, cuts the range by 9.09 %.
- Unlike a petrol car, an electric vehicle can recover energy in braking, so stop-start driving may use less energy per km than steady high-speed driving, and the figure should always be quoted with the driving cycle.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (km) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Eusable Usable battery energy | 5 to 150 kWh | 27.78 | 833.3 | 805.6 | +10% | +10 % |
| ed Energy consumption | 0.1 to 0.4 kWh/km | 150 | 600 | 450 | +10% | −9.09 % |
Sweep of Energy consumption
| Energy consumption (kWh/km) | Ideal range (km) |
|---|---|
| 0.1 | 600 |
| 0.1375 | 436.4 |
| 0.175 | 342.9 |
| 0.2125 | 282.4 |
| 0.25 | 240 |
| 0.2875 | 208.7 |
| 0.325 | 184.6 |
| 0.3625 | 165.5 |
| 0.4 | 150 |
Sweep one variable
Variables and how each one contributes
Ideal range
What the equation gives you. Everything else feeds it.
Usable battery energy
The usable battery energy, in kWh: the nameplate capacity less the reserve the battery management system holds back. Directly proportional: a bigger usable battery gives a proportionally longer range. Raising it by 10 % (to 66) moves the result by +10 %, from 333.3 to 366.7 km.
Energy consumption
The average energy consumption, in kWh per km. Typical cars use 0.15 to 0.25 kWh/km, and heavy vehicles several times more. Inversely proportional: it is the lever that speed, weather and driving style act on. Raising it by 10 % (to 0.198) moves the result by −9.09 %, from 333.3 to 303 km.
Worked example with the values above
- Energy per 100 km: ed × 100 = 0.18 × 100 = 18 kWh.
- Range: d = Eusable / ed = 60 / 0.18 = 333.3 km.
- drange = 333.3 km (207.1 miles).
Assumptions and limits
- A constant average consumption over the whole journey, taken at the battery terminals.
- The full usable energy is available, with no reduction from cold, ageing or reserve limits.
Common mistakes
- Using the nameplate capacity instead of the usable capacity.
- Using a consumption figure measured at the wall socket (which includes charging losses) as if it were the battery-terminal figure.
Statistics and uncertainty
The range is the ratio of two uncertain numbers. The usable energy declines with battery age and temperature, by about 10 to 30 % in cold weather, and consumption varies by 30 % or more between city and motorway driving. A quoted range is therefore only meaningful for a stated test cycle; the 2 % tolerance of this formula is much smaller than the real-world spread.
Where it is used
- Sizing a battery for a target range.
- Converting a quoted consumption figure into distance, or the reverse.
Maths you need
- Energy units: kWh and kJ: 1 kWh = 3.6 MJ
- Averages: consumption as energy per distance