Voltage Across a Capacitor: Formula and Examples

The voltage across a capacitor is the stored charge divided by its capacitance: V = Q / C. Enter charge and capacitance to calculate the voltage; this calculator returns volts, with charge in coulombs and capacitance in farads.

Formula

The basic capacitor relationship is V = Q / C, where:

• V is the voltage across the capacitor, measured in volts (V).
• Q is the magnitude of charge on either one of its plates, measured in coulombs (C). The plates carry equal and opposite charges, +Q and −Q.
• C is capacitance, measured in farads (F).

A farad is one coulomb per volt, so the units are consistent: C / (C/V) = V. The equation also appears as Q = CV, which is useful when charge or capacitance is the unknown. This simple form describes a capacitor with a constant capacitance; the relationship between charge and voltage can be more complicated in nonlinear components or changing operating conditions.

Worked Example

Using the calculator’s default values, the charge is 0.001 C and the capacitance is 0.000001 F.

1. Start with V = Q / C.
2. Substitute the inputs: V = 0.001 C / 0.000001 F.
3. Divide: V = 1,000 V.

The calculator displays 1,000.00 V. This is a mathematical result, not a recommendation that a particular capacitor can safely operate at that voltage. Check the component’s specified ratings and the surrounding circuit design.

What the Formula Means

A capacitor stores separated electric charge. Its capacitance describes how much charge it stores for a given voltage: a larger capacitance needs more charge to reach the same voltage. Conversely, for a fixed amount of charge, a smaller capacitance produces a larger voltage. This is why changing either Q or C changes the result: doubling Q doubles V if C stays fixed, while doubling C halves V if Q stays fixed.

For a parallel-plate capacitor in a simple model, capacitance depends on the plate geometry and the insulating material between the plates. Real capacitors may also have tolerances, leakage, and voltage-dependent behavior. The formula uses the actual capacitance and charge at the condition being considered; a printed nominal capacitance is an approximation subject to the component’s specifications.

Changing Voltage Over Time

The charge formula gives the voltage at a particular moment. For a time-varying current, the charge changes as current flows. Since current is the rate of charge transfer, a useful relationship is i = C(dV/dt) for constant capacitance. Here, i is current in amperes and dV/dt is the rate of voltage change in volts per second. Rearranged, dV/dt = i/C: a constant current changes the voltage more slowly when capacitance is larger.

In a simple resistor-capacitor (RC) circuit connected to a steady voltage source, the capacitor voltage does not usually jump instantly from its initial value to the source voltage. It rises or falls over time according to the circuit conditions. The familiar time constant is τ = RC, with resistance R in ohms and capacitance C in farads; after one time constant, an ideal charging capacitor has reached about 63% of its final voltage, starting from zero. That time-dependent result requires circuit information as well as capacitance, unlike V = Q/C.

Units and Common Mistakes

SI units make the calculation straightforward, but capacitor values are often printed with prefixes. Convert them before substituting. One microfarad (µF) is 10⁻⁶ F, one nanofarad (nF) is 10⁻⁹ F, and one picofarad (pF) is 10⁻¹² F. For example, 10 µF is 0.000010 F. Using 10 as though it were a value in farads would give an answer one million times too small.

• Keep units consistent: use coulombs and farads for volts, or convert both inputs correctly.
• Do not confuse charge with current. Charge is measured in coulombs; current is measured in amperes, or coulombs per second.
• Use the charge on one plate as Q, not the sum of the magnitudes on both plates. The two plate charges are equal and opposite.
• Keep enough significant figures during the calculation, then round the final result to suit the precision of the input data.

There is no separate US customary unit needed for this equation: volts, coulombs, and farads are standard electrical units. A value stated in microfarads or nanofarads must still be converted to farads if the charge is entered in coulombs.

When This Calculation Is Useful—and Its Limits

Use V = Q/C when the charge and capacitance are known and you need the voltage implied by those values. It can also be rearranged to find charge (Q = CV) or capacitance (C = Q/V) when the other two quantities are known and the basic model applies. The calculator requires a positive capacitance; a zero capacitance would make division undefined.

The result alone does not establish whether a component is suitable for a real circuit. A capacitor has a rated voltage, and its behavior can depend on factors such as temperature, frequency, and the applied voltage. Circuit voltage can also include transients or alternating components. Treat the calculation as a relationship between charge and capacitance, not as a substitute for checking component data or analyzing the complete circuit. Stored charge can remain after power is removed, so follow appropriate equipment instructions when working with capacitors.

Frequently Asked Questions

What is the formula for voltage across a capacitor?
For constant capacitance, voltage is charge divided by capacitance: V = Q/C. Use coulombs for charge and farads for capacitance to obtain volts.

How do you calculate capacitor voltage from capacitance and current?
Current alone is not enough; you also need elapsed time and the initial voltage. For constant capacitance and constant current, the voltage change is ΔV = IΔt/C, where I is current in amperes and Δt is time in seconds.

Does voltage across a capacitor change instantly?
In an ideal capacitor, an instantaneous voltage change would require an impulse of current. In ordinary circuits, voltage changes over time as charge flows, with the rate depending on current and capacitance.

What happens to capacitor voltage if capacitance increases?
At a fixed charge, increasing capacitance reduces voltage because V = Q/C. If voltage is held fixed instead, the larger capacitor stores more charge.

Can I use microfarads directly in the formula?
Yes, if you adjust the units consistently. The simplest approach is to convert microfarads to farads first: 1 µF = 0.000001 F. With charge in coulombs and capacitance in farads, the result is volts.

Related

• How to Choose a Desk Lamp for a Small Study Desk
• Fixed vs Floating Exchange Rates: What It Means
• Steam Achievement Sets: DLC, Seasonal Progress & Friends

in q | Charge | C | 0.001 | 0
in c | Capacitance | F | 0.000001 | 0
out v | Voltage across capacitor | V | q / c | 2