Capacitor Voltage Formula: V = Q/C Explained

The common capacitor-voltage formula is V = Q/C: voltage equals the charge stored on one plate divided by the capacitance. This calculator works out voltage when you enter charge and capacitance, returning the result in volts; use coulombs for charge and farads for capacitance.

Formula

V = Q / C

• V is the voltage across the capacitor, measured in volts (V).
• Q is the magnitude of charge on either plate, measured in coulombs (C).
• C is capacitance, measured in farads (F).

The relationship can also be rearranged as Q = CV to find charge, or C = Q/V to find capacitance. The calculator uses the first form and requires positive capacitance; charge may be zero or positive because this version reports voltage magnitude. If describing signed circuit quantities, the sign depends on which plate is chosen as the voltage reference.

Worked Example

Using the calculator’s default values, the charge is 0.00001 C and the capacitance is 0.000001 F.

1. Start with V = Q/C.
2. Substitute the values: V = 0.00001 C / 0.000001 F.
3. Divide: V = 10 V.
4. To two decimal places, the result is 10.00 V.

What the Formula Means

A capacitor stores separated electric charge: one conductor has an excess of charge while the other has an equal-and-opposite amount. Capacitance describes how much charge is stored per volt of potential difference. Rearranging that definition, charge divided by capacitance gives the voltage: V = Q/C.

One farad is one coulomb per volt, so the units are consistent: C/F = C/(C/V) = V. In practice, a farad is a large unit for many electronic circuits, so capacitance is commonly stated in microfarads (µF), nanofarads (nF), or picofarads (pF). Convert before using the formula: 1 µF = 10^-6 F, 1 nF = 10^-9 F, and 1 pF = 10^-12 F.

For example, 20 µC of charge on a 10 µF capacitor gives V = 20/10 = 2 V when both values use matching micro-units. Equivalently, convert them to base units: 20 µC = 20 × 10^-6 C and 10 µF = 10 × 10^-6 F, which also gives 2 V.

When This Relationship Applies

V = Q/C is the basic relation for an ideal capacitor with constant capacitance. It is useful for understanding a stored charge, finding the voltage produced by a known charge, and checking circuit calculations. For a fixed capacitor, doubling the charge doubles the voltage; doubling the capacitance at the same charge halves the voltage.

In a real circuit, charge and voltage can change over time as a capacitor charges or discharges. The formula still relates their instantaneous values for an ideal, constant-capacitance component, but it does not by itself describe how quickly those values change. That behavior also depends on the circuit, including resistance and the way the capacitor is connected.

For a capacitor whose capacitance varies with voltage, the simple constant-C calculation may not describe the full relationship. Such components can require a specified capacitance-versus-voltage characteristic or a more detailed model. Use the component’s stated conditions rather than assuming one capacitance value applies everywhere.

Units, Sign, and Common Mistakes

• Mixing prefixes: Do not divide a charge in microcoulombs by capacitance in farads without conversion. Convert both quantities to base units, or use matching prefixes in a ratio where they cancel.
• Confusing charge with current: Charge is measured in coulombs; current is measured in amperes. Current describes charge flow per unit time, not the stored charge itself.
• Using the wrong sign: The amount of charge is often quoted as a positive magnitude. A signed voltage needs a defined reference direction and plate polarity.
• Rounding too early: Keep extra digits during unit conversion and division, then round the final voltage to a sensible precision.

The calculator accepts charge in coulombs and capacitance in farads. Its displayed result is a voltage magnitude rounded to two decimal places. A zero charge gives zero volts; zero capacitance is not a valid input because division by zero is undefined. Negative capacitance is not accepted in this basic model.

Voltage Is Not the Same as Energy

A common follow-up is how much energy a capacitor holds. Voltage alone does not answer that: energy depends on both capacitance and voltage. For a constant-capacitance ideal capacitor, stored energy is E = ½CV², measured in joules. Using Q = CV, equivalent forms are E = ½QV and E = Q²/(2C). These are energy equations, not replacements for V = Q/C.

For instance, a capacitor’s voltage can be calculated from its charge and capacitance, but finding its energy requires either capacitance and voltage, charge and voltage, or charge and capacitance. Keep the units consistent: farads, volts, coulombs, and joules are the SI units in these equations.

Frequently Asked Questions

What is the formula for voltage across a capacitor?
For a constant-capacitance capacitor, voltage magnitude is V = Q/C, where Q is charge in coulombs and C is capacitance in farads.

How do you calculate capacitor voltage from charge and capacitance?
Divide the charge by the capacitance after putting both values in compatible units. The result is in volts.

What happens to voltage if capacitance increases?
At the same stored charge, increasing capacitance reduces voltage, according to V = Q/C. If charge also changes, use its actual value in the formula.

Can I use microfarads and microcoulombs directly?
Yes, their “micro” factors cancel in Q/C, so the numerical ratio gives volts. For other combinations of prefixes, convert carefully or use base units.

Does V = Q/C tell me how long charging takes?
No. It relates charge, capacitance, and voltage, but charging time depends on the circuit and its components. A time calculation needs additional circuit information.

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in q | Charge | C | 0.00001 | 0
in c | Capacitance | F | 0.000001 | 0
out v | Capacitor voltage | V | q / c | 2