# Elementary Math for EV Drivers

You don’t need to understand high school physics to drive an EV, but the world makes a lot more sense if you just know a few things and can do basic multiplications and divisions. Let’s start with two definitions and units

• Energy measured in kilowatt hours (kWh) measures how long you can generate a certain power. Batteries contain Energy/kilowatt hours
• Power, measured in Watts (W) measures how much electric energy flows per time limit. EV chargers provide Watts when charging, and the more Watts the charger has, the more energy will it add to a battery in a given fixed time.
• kilo just means 1000. So 1 kiloWatt is the same as 1000 Watt.

# Batteries, Consumption, and Range

A typical EV in 2021 uses about 200-300wh per mile. Sometimes, the number is given in kWh/100 miles, and 20-30kWh/100 miles. Higher speeds, cold weather, towing, or just going uphill will increase that number.

A typical EV battery in 2021 provides about 50-90 kWh of Energy. Not all of this will be practically usable as very full and very empty batteries degrade faster.

If we use 75kwH of our battery, and drive at 300wh/mile, we can drive 250 miles (75,000 / 300). With a 100kWh battery we could drive 330 miles. But the heavier battery will increase our power consumption, it may take 350wh/mile, and the 100kWh battery will only get us 280 miles.

# Charging

In theory, we can compute charging time by dividing the size of the battery (75kWh) by the power of the charger (e.g. 300kW) resulting in 1/4 of an hour, or 15 minutes. But for complicated chemical and physical reasons batteries get damaged if we charge with that much power. So we charge at max power when the battery is almost empty, and then slowly lower the power to maybe 50kw. The math is still energy/power, but the power changes constantly.

Common fast chargers – or Level 3 chargers – in 2021 can provide 50kw-350kw of power. They will start at their rated charge, and then drop down to 50kw or even less when the battery is reaching full capacity. Electrify America’s and Tesla’s networks have chargers in this range.

The most common chargers provide from about 1kW (Level 1) to about 20kW (Level 2) of power. The good news is that they can keep up that rate, the bad news is that power is very low.

The same math tells us that a 2kW charger will take about 40h to charge an 80kWh battery. A 12kW charger will take 5h to charge a 60kWh battery. A 20kW charger can chage 60kWh in 3h. Many of the smaller charging stations in supermarkets etc. are in this category.

# Wall Outlets

For charging from regular outlets, or when thinking about installing a charger, we need two more definitions:

• Current, measured in Ampere (A) indicates how much electricity flows. The higher the current, the more Amps, the faster your battery charges.
• Voltage, measured in Volts (V) indicates how much pressure there is. More voltage generates more current (everything else being the same).

The power/Watts of an outlet charging solution can be simplified to the multiplication of Current/Amperes with Voltage/Volts. If you double the Current/Ampere you double the Power/Watts. If you double the Voltage, you also double the Power.

What does that mean?

In the US, a standard household socket provides 120V of Voltage at 15Amp. The 15A is peak current, and we should only use about 80% for sustained load, which puts us at 12A.

• 12A at 120V will give us 1440 W (Watts) of power. This is about what a micro wave oven uses.
• If we charge at 1400W for one hour, we will use
1400 W * 1 hour = 1400 Wh = 1.4kWh of energy.
• A car that uses about 280W for one mile ends up with about 5 miles/hour. Charging 12h a day generates 60 miles of driving per day.
• My Tesla has a 75kWh, so it will take about 50h of charging to go from 0% to 100% (one pretty much never does that, though)

Last Updated on August 3, 2021.