EV Range and Charging, From First Principles
After reading this you can predict how far a real electric car goes at the speed you actually drive, in the weather you actually have, and how long it takes to put those kilometres back in.
An EV's headline range is measured under gentle laboratory conditions. On a cold motorway at 130 km/h with the heater running, the same car can lose a third of that number. This article shows you exactly where those kilometres go, using arithmetic you can check by hand.
What the model does and one quick hook
Give the simulator a usable battery size and a consumption figure at 90 km/h. It scales that consumption to your cruising speed, adds a temperature penalty, adds cabin heating or cooling, and adds a payload term. Divide the battery by the resulting consumption and you have range. Then it does the charging side: AC time to full, a DC 10 to 80% estimate, and how far a 15-minute stop gets you.
The hook: a 60 kWh car rated at 160 Wh/km looks like a 375 km car. Drive it at 130 km/h in freezing weather with the heater on and real range drops toward 230 km. Nothing is broken. The physics is entirely predictable, and the sections below reproduce that number step by step.
When this is the right tool, and when it is not
Use it to plan a specific trip, to compare two cars on the driving you actually do, or to decide whether a charging stop is worth the detour. It answers "will I make it" and "how long do I wait" with honest numbers rather than the optimistic sticker.
Do not treat the output as a guarantee. The model uses one consumption curve shape for all cars and a resistive-heater assumption for cold weather. A car with a heat pump does better in winter. Hilly terrain, strong headwinds and roof boxes are not modelled directly, though you can fake a headwind by raising the cruising speed and a roof box by raising the base consumption.
Every figure here is deterministic. Two people entering the same inputs get the same range to the kilometre. The uncertainty lives in your inputs, especially the base consumption, not in the arithmetic.
The speed formula and why aerodynamics dominates
Two forces resist a moving car. Rolling resistance and electronics draw a roughly constant power per kilometre. Aerodynamic drag grows with the square of speed, because you both hit air faster and hit more of it per second. The model splits consumption so 55% is the constant part and 45% scales with speed squared, calibrated at 90 km/h:
Here C(v) is consumption in Wh/km at speed v in km/h, and C_{90} is your baseline consumption at 90 km/h. At v = 90 the bracket is 0.55 + 0.45 = 1.0, so C = C_{90} exactly. At 130 km/h the bracket is 0.55 + 0.45 \cdot (1.444)^2 = 0.55 + 0.939 = 1.489, a 49% increase in Wh/km over the 90 km/h figure.
This is the single most important fact about EV range. A petrol engine is wasteful at low load, so cruising faster barely dents its efficiency. An EV is efficient everywhere, so extra drag shows up directly as lost range. The curve below shows how sharp the climb is.
Temperature, heating and payload
Cold hurts an EV three ways. Battery chemistry slows down, so usable energy and efficiency drop. The cabin needs heat, and a resistive heater burns real kilowatts. The model captures the chemistry part as a temperature multiplier on consumption:
Between those points the multiplier interpolates smoothly. Above 25 °C air conditioning adds a smaller penalty. The cabin heater is separate and blunt: below 5 °C it draws a steady 1.5 kW. At 110 km/h you cover 110 km per hour, so 1.5 kW spread over 110 km adds 1500 / 110 \approx 13.6 Wh/km. The slower you drive, the more heating costs per kilometre, because the heater runs on the clock while distance accrues slowly.
Payload adds about 2% to consumption per 100 kg, from extra rolling resistance and the energy to accelerate more mass. Four passengers and luggage at 320 kg add roughly 6.4%.
A worked example that reproduces the demo
60 kWh, 160 Wh/km, 110 km/h, 10 °C, 80% highway
These are the demo button values: battery 60, base 160, speed 110, temp 10, climate off, highway 80, payload 0, ac_kw 11, dc_kw 120.
- Highway consumption at 110 km/h: bracket is 0.55 + 0.45 \cdot (110/90)^2 = 0.55 + 0.45 \cdot 1.494 = 1.222. So 160 \times 1.222 = 195.6 Wh/km.
- City consumption at 50 km/h: bracket is 0.55 + 0.45 \cdot (50/90)^2 = 0.55 + 0.139 = 0.689. So 160 \times 0.689 = 110.2 Wh/km.
- Blend 80% highway, 20% city: 0.8 \times 195.6 + 0.2 \times 110.2 = 156.5 + 22.0 = 178.5 Wh/km.
- Temperature at 10 °C: the multiplier is about 1.05, giving 178.5 \times 1.05 \approx 187.4 Wh/km. Climate is off and payload is zero, so nothing else is added.
- Range: 60{,}000 / 187.4 \approx 320 km. (The pure-110 km/h number quoted earlier, 315 km, sits just below because it drops the efficient city share.)
Now charging. AC at 11 kW with 90% efficiency delivers 11 \times 0.9 = 9.9 kW into the battery, so a full 60 kWh charge takes 60 / 9.9 \approx 6.1 hours. DC 10 to 80% moves 70% of 60 kWh, which is 42 kWh. Below 50% the car pulls the full 120 kW peak; above 50% the power tapers. The blended average across 10 to 80% is roughly 100 kW, giving about 42 / 100 \times 60 \approx 25 minutes. A 15-minute splash from a low state of charge near full power adds around 120 \times 0.25 = 30 kWh, worth about 30{,}000 / 187.4 \approx 160 km.
Reading the DC charging curve
Fast charging is not constant. Batteries accept high power when nearly empty and taper as they fill, to protect chemistry and manage heat. The model holds peak power flat to 50% state of charge, then tapers linearly to 20% of peak at 100%:
This is why road-trip advice says stop at 80%. From 80 to 100% you add 20% of the battery at an average near 40 kW, taking about as long as 10 to 50% did at full power. Better to drive on and charge again.
Common mistakes
The biggest error is trusting the WLTP or EPA sticker as a planning number. Those are gentle averages. Enter your own base consumption instead. A compact EV sits around 140 to 170 Wh/km at 90 km/h, an SUV around 180 to 230.
Do not forget that heating cost per kilometre rises as you slow down. A 1.5 kW heater over 50 km/h city driving adds 1500 / 50 = 30 Wh/km, more than double the 13.6 Wh/km it adds at 110 km/h. Cold city driving with the heater on is where EVs feel weakest.
Two more traps. Setting cruising speed too low flatters the car: real motorway traffic runs faster than the speed limit sign. And a heat pump car in winter beats this resistive model noticeably, so treat the cold-weather range as a pessimistic floor if your car has one.
Related tools
If you are weighing what electricity costs to run at home, including whether charging overnight and heating your house on a night tariff pays off, see the Home Heating Cost Simulator. The same kilowatt-hour arithmetic applies to both the car and the house.
Frequently asked questions
Why does my EV lose so much range on the motorway?
Aerodynamic drag grows with speed squared. Going from 90 to 130 km/h raises consumption by about 49% in this model, so range drops by roughly a third. A petrol car hides this because it is already inefficient at low load.
How much range does cold weather really cost?
Two effects stack. Battery chemistry adds up to 35% to consumption at −10 °C. Below 5 °C a resistive cabin heater adds a further 1.5 kW, worth 14 to 30 Wh/km depending on speed. Combined, winter range can fall 25 to 40% versus a mild day.
Should I charge to 100% before a trip?
Only if you need the range to reach the next charger. On the road, stop at 80%. Above that the power tapers below half of peak, so the last 20% takes as long as a much larger chunk earlier in the charge.
Why is AC charging so much slower than the charger rating?
Some energy is lost as heat in the onboard charger and cabling, modelled here at 90% efficiency. An 11 kW charger delivers about 9.9 kW into the battery, so a 60 kWh pack takes about 6.1 hours from empty rather than 5.5.
What base consumption should I enter?
Use a mild-weather figure at a steady 90 km/h. Compact EVs land around 140 to 170 Wh/km, SUVs around 180 to 230. If your dashboard shows a lifetime average, adjust it down slightly, since city driving pulls the average below the 90 km/h value.
Related tools
Home Heating Cost Simulator
What heating really costs — and whether the night setback pays.
3D Model Viewer (STL/OBJ)
Preview STL and OBJ files in 3D — orbit, measure and inspect before printing.
Aspect Ratio Calculator
Simplify W:H, match common ratios, scale sizes.
Cooking Measurement Converter
Cups ↔ grams with per-ingredient densities.
DPI & Pixel Size Calculator
Screen PPI, and pixels ↔ physical print size.
Fuel Economy Converter
MPG (US/UK) ↔ L/100 km ↔ km/L in one step.