Coulombs to Nanocoulombs

What the nano prefix does to a coulomb

The conversion is a straight power of ten, so it has no rounding in it at all. The prefix nano means one billionth, and the NIST table of metric prefixes lists nano as 10^-9. That single line gives you the whole conversion:

• 1 nC = 10^-9 C, one billionth of a coulomb
• 1 C = 10^9 nC = 1,000,000,000 nC

To go from coulombs to nanocoulombs, multiply by 10^9. To go back, divide by 10^9. Nothing about pi or a measured constant enters into it, because the prefix is defined by the number of zeros, not by an experiment.

The same idea shows up in NIST Special Publication 811, Chapter 4 (the Guide to the SI, 2008), which states that SI prefixes refer strictly to powers of 10, and in the SI Brochure, 9th edition (2019), which lists the coulomb as a derived SI unit with the symbol C. Once the prefixes are in place, the coulomb and nanocoulomb are the same quantity at a different scale, like meters and kilometers.

Worked examples, checked by hand

Take 0.00000025 C. Multiply by 1,000,000,000 and the decimal point moves nine places to the right: 0.00000025 C = 250 nC. That is the same charge as 0.25 microcoulombs and 250,000 picocoulombs. A few more, all done the same way:

• 0.0000000042 C = 4.2 nC
• 0.000001 C = 1,000 nC, which is 1 microcoulomb
• 0.001 C = 1,000,000 nC, which is 1 millicoulomb
• 1 C = 1,000,000,000 nC

Going the other way, divide by 10^9, or move the decimal nine places left: 4.2 nC = 0.0000000042 C and 250 nC = 0.00000025 C. The calculator above does both directions, so you can type the number you have and read the one you need.

One habit saves time: write the number in exponent form before you convert. 2.5 x 10^-7 C becomes 2.5 x 10^-7 x 10^9 nC = 2.5 x 10^2 nC = 250 nC, and the exponents tell you the answer is a few hundred rather than a few million.

Common charges in every scale

The table lines up the same charge in four units. The last column counts how many elementary charges that is, using the exact value of the electron charge, 1.602176634 x 10^-19 C, which the NIST CODATA entry for the elementary charge lists as an exact value since the 2019 redefinition of the SI.

Read the nC column from the top and you can see where each prefix lands: every step down the table divides the number by 1,000. A nanocoulomb suits small static charges and the charge one sensor element picks up.

Where nanocoulombs turn up in real work

Static electricity sits in this range. The introductory physics notes from Oregon State University note that the charge produced by rubbing two objects together typically runs from nanocoulombs down to picocoulombs, which is why a rubbed balloon or a plastic ruler can hold a few nC and still be felt as a shock.

Power electronics use the same scale. Gate charge is the charge a transistor needs to switch on, and most datasheets quote it in nanocoulombs. The MIT gate drive application note works two examples: switching a 12 A, 80 V device takes about 15 nC of gate charge, and a 100 kHz converter driven at 14 V needs about 27 nC.

Capacitors follow the rule Q = C x V. A 10 pF part at 25 V stores 10 x 10^-12 x 25 = 2.5 x 10^-10 C, which is 250 pC, or 0.25 nC. Small capacitors at low bias sit in the same range.

Charging a battery works at the opposite end of the scale. A phone taking 2 A for one hour moves 2 x 3600 = 7,200 C, and in nanocoulombs that is 7.2 x 10^12 nC, a number with 13 digits. This is why charge meters for batteries report ampere-hours, a different unit built from current and time.

Current and time: building a charge from a current

Current is charge per unit time, so Q = I x t. That is the easiest way to get nanocoulombs from a circuit, since current and time are usually the numbers you already have.

Worked example: a sensor draws 2 µA for 100 µs. Convert both to base units first: 2 x 10^-6 A and 100 x 10^-6 s. Multiply: 2 x 10^-6 x 100 x 10^-6 = 2 x 10^-10 C. Convert to nanocoulombs: 2 x 10^-10 x 10^9 = 0.2 nC. The calculator has this built in as well, so you can change the current or the time and read the charge.

The nC column shows a pattern: nano is the natural unit whenever a current in the microamp range acts for a time in the microsecond range, because micro times micro is 10^-12, one step of 1,000 from nanocoulombs.

What a nanocoulomb does to a force

Coulomb's law, F = k q1 q2 / r^2, multiplies two charges together, so cutting one charge down by a factor of 1,000 cuts the force down by a factor of 1,000,000. The constant k is 8.9875518 x 10^9 N m^2/C^2, worked out from the vacuum permittivity of 8.8541878188 x 10^-12 F/m that appears in the 2022 CODATA values published by NIST.

Check one row by hand: two charges of 250 nC, which is 0.00000025 C each, at 1 cm, give F = 8.9875518 x 10^9 x (2.5 x 10^-7)^2 / (0.01)^2 = 8.9875518 x 10^9 x 6.25 x 10^-14 / 1 x 10^-4 = 5.62 N. That is a real push, the kind you can feel from a charged object, which tells you how much charge has to be present for static electricity to matter.

Nano charges interact weakly at a distance: you need micro or milli units before forces become obvious in the lab. The Coulomb's law calculator on this site runs the same formula with any pair of charges.

Counting the electrons in a nanocoulomb

Charge comes in fixed steps, and the elementary charge e = 1.602176634 x 10^-19 C has been exact since 2019. Divide the charge by e and you get the count of electrons.

For 1 nC: 10^-9 / 1.602176634 x 10^-19 = 6.241509074 x 10^9, so one nanocoulomb carries 6,241,509,074 electrons, about 6.24 billion of them. For 250 nC that becomes 1,560,377,268,615 electrons, and one coulomb is 6.241509074 x 10^18 electrons.

The count also runs the other way. One electron carries 1.602176634 x 10^-19 C, which is 1.602176634 x 10^-10 nC, so a hundredth of a nanocoulomb is about 6.24 million electrons. A charge of 0.001 nC still means 6,241,509 electrons, so a reading printed to three decimals in nC is a whole number of particles underneath.

Charge figures also come out as multiples of e in careful measurements. If a lab reports 4.2 nC, that is 4.2 x 10^-9 C, which is 26,214,338,113 electrons once you round to a whole electron.

Rounding, formatting and the mistakes to avoid

Nanocoulomb values are usually written in exponent form or with all the leading zeros, and both are easy to get wrong. These are the same charge written three ways:

Three errors cause most of the trouble. First, moving the decimal the wrong way: converting to nanocoulombs means moving the point right, not left. Second, mixing up micro and nano, which differ by a factor of 1,000. Third, reading 10^-9 as 10^-6 because the number looks similar.

How many digits to keep depends on the job. For a charge quoted to two or three significant figures, write 250 nC or 4.2 nC. For a lab value that came out of a measurement, keep the digits your instrument gave you and let the reader judge. The calculator prints nanocoulombs, microcoulombs, picocoulombs and the electron count together so you can pick the scale that fits the job.

One last check: a negative charge keeps its sign. A value of −250 nC is −0.00000025 C, and the minus sign carries straight through every conversion on this page.