Potential difference (voltage) is the energy transferred per unit charge moved between two points — V = W/Q, measured in volts, where one volt is one joule per coulomb. This free calculator solves for the potential difference, the energy transferred or the charge, in any unit, and shows every step of the working.
Potential difference — everyday "voltage" — measures how much energy each unit of charge gives up (or gains) between two points. Its definition is simply energy divided by charge: V = W/Q, where W is the energy transferred in joules and Q is the charge moved in coulombs. The answer is in volts, and one volt means exactly one joule of energy is transferred for every coulomb of charge that passes. That is why a 12 V supply delivers 12 J to every coulomb, no matter how many coulombs actually flow.
There are three steps. First, decide what you want — the potential difference V, the energy W, or the charge Q — and pick it in the calculator's Solve for menu. Second, enter the values you know: energy in joules, charge in coulombs, and voltage in volts (prefixed units such as mV, kJ and µC are converted for you). Third, read the answer with the worked steps, which show the rearranged formula, your numbers substituted in, and the result with its unit. The three rearrangements are V = W/Q, W = Q·V and Q = W/V.
Two relationships are worth feeling directly. Voltage rises in step with the energy — double the joules moved for the same charge and the potential difference doubles — but falls as the charge grows: spread the same energy over twice the charge and each coulomb gets half as much. Crucially, the voltage between two fixed points does not depend on how much charge you move; it is energy per coulomb, an intrinsic property of the two points. If you know the current and resistance instead of the energy, reach for the Ohm's Law calculator (V = I·R); to work with the charge itself, see the electric current calculator, or look up a term in the physics glossary.
A charge of Q = 2.0 C moves between two points and transfers W = 24 J of energy. The potential difference is V = W/Q = 24 / 2.0 = 12 V. Rearranging shows the same physics from the other side: moving 5.0 C through 9.0 V transfers W = Q·V = 5.0 × 9.0 = 45 J, and delivering 150 J across a 6.0 V drop requires Q = W/V = 150 / 6.0 = 25 C. Notice the 12 V result is fixed by the energy and charge alone — it would be 12 V whether one coulomb or a thousand crossed the gap.
Potential difference is the quantity a voltmeter reads and the one that drives current through every circuit. It underlies battery and cell ratings, the loop rule that splits voltage across resistors in series, the energy a capacitor stores, and the electrical safety limits that separate a harmless static spark from a lethal shock. Understanding voltage as energy per coulomb — not as something that gets "used up" — is the key idea that makes the rest of circuit theory fall into place.
Potential difference comes out in volts (V), energy in joules (J) and charge in coulombs (C). One volt is defined as one joule per coulomb, so the units are self-consistent: dividing joules by coulombs gives volts directly. The calculator also converts prefixed inputs such as millivolts, kilojoules and microcoulombs to SI before it computes.
This calculator uses the definition of voltage as energy per unit charge, V = W/Q, so it links potential difference to the joules moved per coulomb. The Ohm's Law calculator instead relates voltage to current and resistance, V = I·R. Both give the same potential difference for a given situation, but they start from different measured quantities: energy and charge here, current and resistance there.
Because V = W/Q divides by the charge, and dividing by zero is undefined — no charge has moved, so "energy per unit charge" has no meaning. The calculator returns no result until you enter a charge greater than zero. Charge must also be non-negative when you solve for energy.
Yes, when you solve for energy or charge. A negative potential difference simply means the direction of the drop is reversed relative to your chosen reference, and the sign carries through to the energy or charge. When you solve for the voltage itself from energy and charge, the calculator expects a non-negative energy and a positive charge, so V comes out positive.
Set the “Solve for” menu to W (energy transferred), then enter the charge Q and the potential difference V. The calculator applies W = Q·V and returns the energy in joules — for example, moving 5 C through 9 V transfers 45 J. This is the work done by (or on) the charge as it crosses the potential difference.