Electric Charge Calculator

What a coulomb measures

Electric charge is a quantity, in the same sense that mass and volume are quantities, and the coulomb is its unit. The symbol Q stands for the charge, I for the current, and t for the time the current flows. Every one of those three connects to the other two, and the connection is what the calculator at the top of this page runs.

Current is charge in motion. One ampere is one coulomb passing a point in one second, so a 2 ampere charger moves 2 coulombs every second. The International System of Units ties the ampere to a fixed value of the elementary charge, and the NIST summary of the ampere definition shows how the two units lock together. The BIPM SI base units page lists the same definition for every unit this page uses.

Charge comes with a sign. Electrons carry a negative charge and protons carry a positive one, and the total is what matters. A wire carrying 2 amperes is moving charge of both signs, and the coulomb count describes the net flow through a cross section of that wire.

Charge from current and time

The formula is short: Q = I x t. Charge in coulombs equals current in amperes times time in seconds. A current of 2 amperes flowing for 30 seconds moves Q = 2 x 30 = 60 coulombs through the wire.

Keep the time in seconds. A current of 0.5 amperes running for one hour is 0.5 x 3600 = 1800 coulombs, and entering 1 instead of 3600 in the time box will understate the charge by a factor of 3,600. The table below shows how fast ordinary currents stack up.

The starter motor row is the one that surprises people. Three seconds of cranking moves more charge than ten minutes of an LED, because current and time count equally in the product. Halving the time halves the charge, just as halving the current does.

Counting electrons in a charge

A coulomb is a huge number of electrons. The elementary charge, written e, is the charge of one electron: 1.602176634 x 10^-19 coulombs, fixed by the 2019 revision of the SI. The NIST constants reference lists that value among the exact defining constants.

Divide the charge by e to count the particles: 1 coulomb contains 6.24 x 10^18 electrons. The 60 coulombs from the example above is 3.74 x 10^20 electrons, a number with 21 digits. Nothing in the wire slows down to arrange those electrons; they drift along at walking pace, and the count is a bookkeeping result.

Notice how wide the range is. Static shocks deal in nanocoulombs and microcoulombs, chargers deal in hundreds of coulombs, and battery labels deal in thousands. The electron count just shifts the decimal point; the physics underneath is the same product of charge and count.

Amp-hours on a battery label

Battery labels use amp-hours rather than coulombs, and the two connect directly: 1 amp-hour is 1 ampere flowing for 1 hour, which is 1 x 3600 = 3,600 coulombs. A phone battery marked 5,000 mAh holds 5 amp-hours, or 18,000 coulombs of charge.

Charge alone does not tell you the energy, because energy is charge times voltage. Multiply 18,000 coulombs by a nominal 3.85 volts and the phone battery stores 69,300 joules, which is 19.25 watt-hours. Two batteries with the same amp-hour rating store different energy if their voltages differ, which is why laptop and tool batteries quote watt-hours as well.

The amp-hour figure is a rating measured under test conditions, so the real deliverable charge runs lower in cold weather and at high discharge rates. The amp-hour calculator converts between ratings, and the battery charge time calculator turns a rating and a charger wattage into hours.

Charge stored in a capacitor

Capacitors store charge without moving it through a circuit loop, and their formula is Q = C x V: capacitance in farads times voltage in volts. A 100 microfarad capacitor charged to 12 volts holds 100 x 10^-6 x 12 = 0.0012 coulombs, which is 1.2 millicoulombs.

Stored energy is a different product: one half of capacitance times voltage squared. For the same capacitor that is 0.5 x 0.0001 x 144 = 0.0072 joules, or 7.2 millijoules. Doubling the voltage doubles the charge but quadruples the energy, which is why high voltage capacitors demand respect.

The capacitance page works through the charge and energy formulas in detail, and the capacitor calculator adds reactance for circuits driven by alternating current.

Positive, negative and conserved

Charge is never created or destroyed in an everyday circuit; it only moves. Rub a balloon on hair and electrons transfer to the balloon, which ends up negative while the hair ends up positive, and the two together still sum to the original zero. That bookkeeping rule, called conservation of charge, is why every current that enters a junction has to leave it.

Static shocks put tiny charges on the move. The human body holds roughly 100 picofarads of capacitance, so at a 5,000 volt doorknob potential it carries 0.0001 x 10^-6 x 5,000 = 0.5 microcoulombs, or 500 nanocoulombs. That is about 3 x 10^12 electrons, and the discharge lasts a fraction of a millisecond. Tiny charge, real sting.

Signs matter when charges combine. Two objects at +3 microcoulombs and -1 microcoulomb together hold +2 microcoulombs, and a wire that connects them will move 1 microcoulomb of electrons until both reach +1. The same arithmetic runs at every scale from a doorknob to a lightning bolt.

Force between two charges

Charge does more than flow; it also pulls and pushes. Coulomb's law gives the force between two point charges: F = k x Q1 x Q2 / r^2, with the constant k equal to 8.99 x 10^9 newton meters squared per coulomb squared. Two charges of 1 coulomb sitting 1 meter apart push on each other with 8.99 x 10^9 newtons, which is why a bare coulomb is a laboratory scale amount and not a pocket amount.

Scale the charges down and the numbers turn friendly. Two 1 microcoulomb charges 10 centimeters apart exert 0.899 newtons, about the weight of a small apple. The distance squared in the denominator is what makes static forces fade fast: at 1 meter the same pair pulls with 0.00899 newtons, a hundred times weaker.

The Coulomb's law calculator runs that formula directly, and the electric field calculator converts a single charge into the field it produces at a distance.

Where these numbers stop being useful

Every result on this page assumes the current or the capacitance holds steady for the whole interval. Real chargers taper near full, capacitors leak through their dielectric, and battery labels reflect a nominal voltage rather than the exact terminal voltage under load. Treat the outputs as estimates for a stated interval, not as measurements.

Time units are the most common source of error. The formula needs seconds, so 1 hour is 3,600 seconds and 1 minute is 60. Entering minutes directly understates the charge by a factor of 60, and the mismatch will not produce an error message, just a quietly wrong number.

Safety sits outside the arithmetic. A capacitor can hold a lethal charge long after equipment is unplugged, and mains voltage kills. Use this page to size intuition, check a homework result or sanity check a datasheet, and leave service work on energized equipment to qualified people. Nothing here is electrical safety advice.