Coulombs to Picocoulombs

Why one coulomb is a trillion picocoulombs

The conversion is a straight power of ten, so it has no rounding in it. The prefix pico means one trillionth, and the NIST table of metric prefixes lists pico as 10^-12. That single definition gives the whole conversion:

• 1 pC = 10^-12 C, one trillionth of a coulomb
• 1 C = 10^12 pC = 1,000,000,000,000 pC
• 1 pC = 0.001 nC, so nano sits three places above pico

To go from coulombs to picocoulombs, multiply by 10^12. To go back, divide by 10^12. Nothing measured enters the arithmetic, because the prefix is fixed by definition. NIST Special Publication 811, the United States guide to the SI, states that prefixes refer strictly to powers of 10, and the SI Brochure, 9th edition (2019), lists the coulomb itself as a derived SI unit with the symbol C.

The scale matters as much as the factor. A coulomb is an enormous charge for electronics: one pC is to one C what one gram is to a million metric tons. Instruments that work with single pixels, single particles or single picoamp currents live down here, and datasheets quote them in pC because writing twelve zeros invites mistakes.

Converting C to pC by moving the decimal point

Multiplying by 10^12 moves the decimal point twelve places to the right. Take 0.000000000125 C: after the shift it reads 125 pC. The shortcut that causes the fewest errors is to work in exponent form: add twelve to the exponent and leave the digits alone. 1.25 x 10^-10 C becomes 1.25 x 10^2 pC, which is 125 pC.

Going the other way, subtract twelve from the exponent. 3.4 x 10^-11 C is 34 pC, and 34 pC written out in full is 0.000000000034 C. A check that catches most slips: picocoulomb figures are always bigger than the coulomb figure for the same charge, by a factor of a trillion. If your result got smaller, the move went the wrong way.

One more habit helps when the charge is tiny: convert through nanocoulombs. 1 pC is 0.001 nC, so 45 pC is 0.045 nC and 0.045 nC is 4.5 x 10^-11 C. Working one prefix at a time keeps the decimal point where you can see it, and the calculator above prints every prefix at once so you can compare.

A pC conversion table you can check in your head

The table lists the same charges in four units. The last column counts the electrons behind each charge, using the exact value of the elementary charge, 1.602176634 x 10^-19 C, which the NIST CODATA entry for the elementary charge has listed as an exact value since the 2019 redefinition of the SI.

Every row one step down multiplies the pC figure by ten. Every column to the right is the previous column divided by 1,000. Read the bottom row as the boundary of the scale: a full coulomb is a trillion times the smallest charge in the table, which is why the two ends of the table never share a datasheet.

Where picocoulombs show up: pixels, detectors and front ends

Image sensors count electrons one pixel at a time. A pixel that has collected 10,000 electrons holds 10,000 x 1.602176634 x 10^-19 = 1.6 x 10^-15 C, which is 0.0016 pC. A pixel well that fills with six million electrons approaches 1 pC. Sensor readout chains therefore talk about electrons and picocoulombs as two views of the same stored charge.

Radiation detectors work the same way. An ionization chamber that has collected 1 pC has separated about 6.24 million ion pairs, one electron of charge each, and the electrometer in front of it is specified in pC because that is the whole signal. Photodiode receivers follow the same pattern: the front end integrates charge from a current that runs for a fixed window, and reports the result as a charge in pC.

Forces at this scale are small but measurable. Two charges of 1 pC held 1 mm apart push on each other with F = 8.9875517923 x 10^9 x (1 x 10^-12)^2 / (0.001)^2 = 8.99 x 10^-9 N, using the Coulomb constant from the CODATA 2018 constants published by NIST. That is millions of times lighter than a grain of salt, which is why pC charges need sensitive electronics rather than a meter stick to be noticed.

Charge from current: the picoamp-second

Current is charge per unit time, so Q = I x t. At the picocoulomb scale the natural current unit is the picoamp: 1 pA running for 1 s moves 1 x 10^-12 A x 1 s = 1 pC. The arithmetic is symmetric, so any pair of current and time multiplies out the same way.

• 250 pA for 4 s = 1,000 pC, which is 1 nC
• 5 pA for 200 s = 1,000 pC as well
• 1 nA for 1 ms = 1 pC, since 10^-9 x 10^-3 = 10^-12

This is why instrumentation datasheets quote input bias currents in pA and charge per sample in pC: the two numbers describe one trade. A smaller bias current lets you integrate longer before the charge reaches the level you care about. If a front end leaks 1 pA and you need the reading to stay under 10 pC of drift, you have about 10 seconds before the drift alone fills the budget.

The same rule works in reverse when you audit a design. A charge of 34 pC that arrived over 3.4 s means the average current was 10 pA. Convert the charge first, divide by the time, and the current falls out in pA, ready to compare with the specification.

The table turns the current and time you already have into a charge in picocoulombs. Multiply the current in amperes by the time in seconds, then multiply by 10^12 to get picocoulombs.

Read the pC column as the size of the packet of charge moving through the wire. A picoamp of leakage current for a second is a picocoulomb, which is why instrument datasheets quote picoamps and picofarads side by side.

How many electrons a picocoulomb holds

Charge comes in fixed steps of the elementary charge, e = 1.602176634 x 10^-19 C, exact since 2019. Divide the charge by e to get the count. For 1 pC: 10^-12 / (1.602176634 x 10^-19) = 6.241509074 x 10^6, so one picocoulomb carries 6,241,509 electrons.

The count scales without surprises. 34 pC holds about 212 million electrons, 125 pC holds about 780 million, and 1,000 pC holds 6.24 billion. Going down instead of up, a single electron is 1.602176634 x 10^-19 C, which is 1.6 x 10^-7 pC, so a million electrons gather only 0.16 pC.

That ratio explains the vocabulary of sensor engineering. When a camera review says a pixel collects 30,000 electrons of noise, you can translate: 30,000 x 1.602176634 x 10^-19 C is 4.8 x 10^-15 C, or 0.0048 pC. Any charge quoted in electrons converts to pC with one multiplication, and any charge in pC converts back with one division.

Dividing the charge by the exact elementary charge, 1.602176634 x 10^-19 C, gives the electron count. The numbers below are rounded to three significant figures.

One picocoulomb is a few million electrons, so a single stray touch on a sensitive input is enough to move the reading.

pC is not pF: the mix-up that slips past a design review

Picocoulomb and picofarad share a prefix and differ in what they measure, which is enough for a costly swap. A picofarad is a capacitance, a property of a component. A picocoulomb is a charge, a quantity of electrons. The bridge between them is Q = C x V: a 100 pF capacitor is not 100 pC of charge, it holds 100 pF times whatever voltage sits across it.

Worked example: 100 pF at 5 V holds 100 x 10^-12 x 5 = 5 x 10^-10 C = 500 pC. The same capacitor at 1.8 V holds 180 pC. So the pF figure fixes the pC figure only after you name the voltage.

The confusion runs both ways. A datasheet line that reads "charge injection, 3 pC" is telling you how much charge a switch dumps into a circuit each time it opens or closes, and the number has nothing to do with the 3 pF of capacitance listed two lines above. Keep the two apart by asking one question: does this number change if the voltage changes? If yes, it is a capacitance; if no, it is a charge.

Writing pC values so nobody misreads them

Picocoulomb numbers live where zeros pile up, so pick one of two formats and stay with it. The first is scientific notation: 4.5 x 10^-11 C instead of 0.000000000045 C. The second is a prefix big enough to keep the digits short: 0.045 nC says the same thing with fewer leading zeros. What to avoid is a bare decimal with eleven places, because a miscount of one zero is an error of a factor of ten.

Sensor outputs add one more convention: charge sensitivity. Piezoelectric force sensors are rated in pC per newton, so a 20 pC/N sensor under a 50 N load produces 20 x 50 = 1,000 pC, which is 1 nC. The unit tells you the input (force) and the output (charge) in one line, and the multiplication finishes the conversion.

Keep the sign through every step. A charge of -125 pC is -1.25 x 10^-10 C, and in a charge amplifier the sign decides which way the output rails. Rounding follows the source: a value quoted as 34 pC carries two significant figures, so 33.9999 pC is false precision, not a better answer.