Physics & Mechanics

Voltage Calculator

Calculate electric potential difference (voltage) given energy and charge, or use Ohm's law with current and resistance.

J
C
Voltage (V)
5

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Energy Per Charge

While the previous calculator found voltage based on distance from a particle, the most fundamental definition of Voltage is the amount of work (Energy) required to move a specific amount of Charge.

One Volt is exactly equal to One Joule per Coulomb. If a battery is rated at $9\text{V}$, it means the battery expends exactly 9 Joules of chemical energy to shove 1 Coulomb of electrons through the circuit.

The Water Pump Analogy

If a circuit is a water slide, Voltage is the water pump at the bottom. The pump does mechanical work to physically lift the water back to the top of the slide. The higher the pump lifts the water, the more potential energy the water has, and the faster it will rush down the slide. A $120\text{V}$ wall outlet is a massive, high-pressure industrial pump, while a $1.5\text{V}$ AA battery is a tiny, weak aquarium pump.

Practical Applications

  • Phone Batteries: Your lithium-ion phone battery operates at roughly $3.7\text{V}$. When you charge your phone, the wall adapter is physically forcing electrons backward into the battery against their will, storing chemical potential energy.
  • Defibrillators: A medical defibrillator charges a massive capacitor up to $3000\text{V}$. This incredibly high voltage is required to force a massive, instantaneous surge of current straight through the natural resistance of the human chest to restart a heart.

The Formula

V=WQ\begin{aligned} V = \frac{W}{Q} \end{aligned}

Where:
V=
Voltage / Potential Difference (Volts, V)
W=
Work or Energy transferred (Joules, J)
Q=
Electric Charge (Coulombs, C)

Example Calculation

A small electric motor does $10 , \text{Joules}$ of physical work to lift a toy car. In doing so, it consumes $2 , \text{Coulombs}$ of electrical charge from the battery pack.

  1. Divide Energy by Charge ($W / Q$): $10 / 2 = 5$.

The voltage required to run this motor is exactly $5 , \text{Volts}$. Every single Coulomb of electrons that passed through the motor surrendered exactly 5 Joules of energy to lift the toy car.

Frequently Asked Questions

A battery contains a finite amount of chemical reactants. It uses these chemicals to do the 'work' of pushing electrons. Once the chemicals are completely used up, the battery can no longer do work, meaning it can no longer maintain a voltage difference. The voltage drops to zero, and the device shuts off.

Yes! A fresh AA battery sitting completely alone on a table has exactly $1.5\text{V}$ of potential difference between its top and bottom. The 'pressure' is there, waiting. But because there is no wire connecting the ends, no electrons can actually flow, so the current is strictly zero.

When electrons flow through a resistor (like a lightbulb), they lose energy as heat and light. If they enter the bulb with 9 Joules of energy and leave with 0 Joules, they 'dropped' 9 Volts across the bulb. The sum of all voltage drops in a loop always equals the total voltage of the battery.