Pack Size in Kilowatt-Hours, Physics in Joules
Everything an electric car tells you about its energy is quoted in kilowatt-hours: a 60 kWh pack, 17 kWh per 100 km, a charging session that added 41 kWh. Everything a physics course tells you about energy is quoted in joules. Bringing the two together is the moment an EV stops being a spec sheet and starts being a machine you can reason about — how much energy is really in that pack, how fast a charger pours it in, and where it goes on the way to the wheels.
Three Numbers That Never Quite Agree
The Pack Rating Is Usable, Not Total
Watt-Hours per Kilometre Is the Honest Range Number
The Meter at Home Counts More Than the Car Gains
Working From Pack Size to Range and Charge Time
Two fields cover most of what an owner or a student actually needs, provided the quantity going in is energy rather than power.
Put the pack or session figure on the kWh side
Type 40, 60, 77 or whatever the brochure claims, and the joule column resolves beside it. A trip works the same way: kilometres times consumption in Wh/km, divided by a thousand, gives the kilowatt-hours that journey costs.
Keep energy and power in separate boxes
A 150 kW charger is a rate, not a quantity — it becomes energy only once multiplied by time. Kilowatts belong nowhere near these fields; kilowatt-hours, the product of the two, are what convert.
Reverse it when the source is already in joules
Physics problems arrive the other way round — kinetic energy at motorway speed, or a regenerative braking figure in joules. The swap arrows put joules on the input side and give back the fraction of a kilowatt-hour it represents.
Add the charging loss at the end
Dividing the converted result by 0.90 approximates what the household meter will record. Doing that after the conversion keeps the pack's stored energy and the electricity you paid for as two clearly separate numbers.
Packs, Journeys and Charging Sessions in Both Units
Pack rows use usable capacity; journey rows multiply distance by a realistic consumption figure. Range in the last column is capacity divided by the stated Wh/km, with no reserve held back.
| Pack or journey | Energy (kWh) | Energy (J) | Range or duration |
|---|---|---|---|
| City car pack | 40 | 144 000 000 | 250 km at 160 Wh/km |
| Mid-size hatchback pack | 60 | 216 000 000 | 353 km at 170 Wh/km |
| Estate or crossover pack | 77 | 277 200 000 | 385 km at 200 Wh/km |
| Large SUV pack | 100 | 360 000 000 | 455 km at 220 Wh/km |
| 30 km commute at 150 Wh/km | 4.5 | 16 200 000 | 1 h 30 min on a 3 kW socket |
| 500 km motorway leg at 200 Wh/km | 100 | 360 000 000 | Two charging stops for most cars |
| 10–80 % on a 77 kWh pack | 53.9 | 194 040 000 | 21.6 min at a flat 150 kW |
| Overnight at 7.4 kW for 8 h | 59.2 | 213 120 000 | Refills almost any pack |
The joule column is the reason nobody quotes it: 216 million is an awkward way to say 60, and every row differs from its neighbours by a factor no driver would sense. Its value is comparative — set 2.16 × 10⁸ J beside a kinetic-energy calculation for the same car at motorway speed and the pack turns out to hold enough for several hundred full-speed accelerations.
What Helps When Comparing Cars and Chargers
Depot-Scale Totals Drop Into Exponent Form
A car pack stays in plain digits with the thousands spaced out, but a depot charging a fleet gets past ten billion joules at around 2 778 kWh, and the answer switches to a power of ten rather than sprawling across the field.
Swap In a Different Trim's Pack Size Mid-Comparison
Overtype 60 with 77 and the joule side has already followed before you reach the end of the number, which makes running down a manufacturer's battery options quicker than opening a second tab for each one.
Joule Digits Ready for the Physics Worksheet
The copy control above each field, or Ctrl+C from within it, returns the bare number with no unit and no spacing — which is what a ½mv² comparison or an energy-balance question actually wants pasted in.
Wh, MJ and MWh From the Same Two Fields
Consumption tables print watt-hours, engineering notes prefer megajoules and a fleet report counts megawatt-hours; all three are a search away in either dropdown without restarting the calculation.
Charging and Range Questions Behind the Pack Figure
A 60 kWh pack in joules — why does nobody quote it that way?
216 million joules, or 2.16 × 10⁸ J. It goes unused for the same reason nobody measures a journey in millimetres: the unit is the wrong size for the job. The joule is defined at human scale — one newton through one metre, about what it takes to lift an apple off a table — while a car battery is an industrial quantity of energy. Every pack on the market would sit between 10⁸ and 10⁹, so the interesting digits get buried under exponents. The kilowatt-hour survives because it multiplies cleanly against a charger's kilowatts and against a tariff in cents, and both of those are numbers a driver acts on.
How does a watt-hour-per-kilometre figure turn into a range?
Divide usable pack energy in watt-hours by consumption in watt-hours per kilometre. A 60 kWh pack is 60 000 Wh, so at 170 Wh/km it covers 353 km; at 220 Wh/km, the sort of figure a heavy car sees in winter at 120 km/h, the same pack manages 273 km. Consumption is the variable that actually decides range, and it is dominated by speed, because aerodynamic drag grows with the square of it. Cold weather compounds the problem twice over: the cells deliver less, and cabin heating draws 1–3 kW that never turns a wheel. This is also why the figure printed on a European window sticker, measured over a cycle averaging well under motorway speed, is optimistic for anyone who lives on a motorway.
Why does my home meter record more than the car gained?
Because several things between the socket and the cells take a share. The onboard charger rectifies alternating current to direct and loses a few per cent as heat doing it. The battery management system, contactors and cooling pumps run throughout the session. Cells warm slightly as they take charge, which is energy that leaves as heat rather than staying stored. And a car left plugged in keeps waking to check its state, adding a slow trickle that no one accounts for. Together these run 8–12 % on a home AC charger, so adding 60 kWh to the pack costs roughly 67 kWh at the meter. DC fast charging bypasses the onboard charger and does rather better, though thermal management then works harder.
How long does 150 kW charging take to add 200 kilometres?
At 180 Wh/km, 200 km needs 36 kWh. A charger holding a genuine 150 kW delivers 1 kWh every 24 seconds, so 36 kWh takes 14.4 minutes on paper. Reality lands somewhat above that, because the peak rate exists only in a window — typically between about 10 and 60 % state of charge — after which the car tapers steeply to protect the cells. Arrive with a warm battery at 15 % and the paper figure is close; arrive at 60 % on a cold day and the same 36 kWh can take twice as long. This is why fast-charging comparisons quote a 10–80 % time rather than a headline kilowatt number, since only the former reflects what the car will actually accept.
How much of the braking energy does regeneration actually return?
Less than the physics allows, but enough to matter. Slowing 1.8 tonnes from 100 km/h to rest releases about 694 000 J of kinetic energy, roughly 0.19 kWh. The motor running as a generator can capture a good share, but the inverter, motor and battery each take a cut on the way in, and a second helping goes to rolling resistance and drag, which were slowing the car regardless. Around 60–70 % of the recoverable energy typically reaches the pack in gentle deceleration, dropping sharply in a hard stop where friction brakes have to take over. Across mixed driving that adds perhaps a tenth to overall efficiency — modest per event, but it is the main reason an EV consumes less in town than on the open road, exactly reversing the pattern a combustion car shows.
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