Capacitors In Series Calculator - Equivalent Capacitance and Voltage Split

A capacitors in series calculator reduces a string of two to ten capacitors to a single equivalent capacitance and explains how the total voltage drops across each element. Use it when you have a chain wired end to end and need the combined capacitance, the reciprocal sum, or each capacitor's share of the supply voltage.

• • Combine a chain of capacitors into one equivalent: Enter two to ten capacitance values and read the single equivalent capacitance for the whole series string in farads, millifarads, microfarads, nanofarads, or picofarads.
• • Plan a capacitor voltage divider: Add a total voltage across the string and read how it distributes across each capacitor, including how the smallest capacitor takes the largest share.
• • Verify a textbook worked example: Enter the 2 mF, 5 uF, 6 uF, 200 nF string and read 186.3 nF as the combined capacitance to compare against class solutions.
• • Sanity-check a hand calculation: Compare the calculator output against a manual 1/C_eq = sum(1/C_i) computation when teaching circuits labs.

Capacitors wired in series share the same charge, so the same Q moves through every element. The supply voltage divides across the string in proportion to each capacitor's inverse capacitance, which makes the equivalent capacitance always smaller than the smallest capacitor in the chain.

Once you have the equivalent series capacitance, the next question is usually how fast that combined capacitor charges through a resistor, and the capacitor charge time calculator takes the same farad value alongside a resistor for RC timing.

The capacitors in series calculator starts with the same-charge rule Q = C_eq x V_total and the per-element voltage equation V_i = Q / C_i. Summing V_i across the string and dividing by Q produces the reciprocal-sum formula that defines the equivalent capacitance.

• C_1, C_2, ..., C_n: Capacitance of each capacitor in the string after converting the selected unit prefix (F, mF, uF, nF, pF) to farads.
• C_eq: Equivalent series capacitance in farads, equal to one divided by the reciprocal sum of every active capacitor.
• V_total: Total DC voltage applied across the series string. When zero, the calculator suppresses the per-capacitor voltage split.
• V_i: Voltage across the i-th capacitor. Computed as V_total x C_eq / C_i, which is the inverse-capacitance weighted share of the supply.

The calculator picks the display unit for the equivalent capacitance from the magnitude of the answer, so a string that resolves to 1.86e-7 F renders as 186.3 nF. Voltage outputs are hidden when the total voltage is zero so the form stays useful for capacitance-only checks.

According to OpenStax University Physics Volume 2, Section 8.2, the reciprocal of the equivalent capacitance of series capacitors is the sum of reciprocals of individual capacitances, every series capacitor carries the same charge Q, and the equivalent is smaller than the smallest capacitance in the network.

As published by All About Circuits, the same-charge rule divides supply voltage across series capacitors in inverse proportion to capacitance, so the 2 mF, 5 uF, 6 uF, 200 nF string sits well below 200 nF.

When the string mixes 2 mF with 200 nF, the capacitance conversion calculator confirms each prefix factor before the reciprocal sum runs, since the math lives or dies on every entry being in farads.

Four concepts make the series rule easier to remember. Once these click, every reciprocal-sum answer reads itself.

The series rule mirrors the parallel-resistor rule and contrasts with the parallel-capacitor rule, which is just a straight sum.

According to HyperPhysics, capacitors connected in series carry the same charge Q, so the equivalent capacitance is always smaller than the smallest capacitor in the string.

Once you know the per-capacitor voltage, the voltage divider calculator can confirm the same divider math from a resistor point of view when you want to compare capacitive and resistive dividers side by side.

Enter the string, the unit, and an optional total voltage. The form rebuilds its capacitor fields from the count selector and shows the equivalent capacitance, the reciprocal sum, and the per-capacitor voltage split.

1. 1 Choose the number of capacitors: Set the count selector between 2 and 10. The form keeps the active rows visible and ignores empty slots beyond the chosen count.
2. 2 Pick the capacitance unit: Select F, mF, uF, nF, or pF. The same unit is applied to every entry, so convert mixed-prefix strings before they are entered or use the capacitance conversion calculator.
3. 3 Enter the capacitance values: Fill the active capacitor rows. Skip a row by leaving it at 0. At least two rows must hold a positive value or the calculator will surface a validation message.
4. 4 Add an optional total voltage: Enter the DC voltage applied across the whole string. Leave it at 0 to hide the per-capacitor voltage split and only read the equivalent capacitance.
5. 5 Read the equivalent capacitance: Equivalent C is shown in the unit that best matches its magnitude, alongside the reciprocal sum and the smallest capacitance as a sanity bound.
6. 6 Review the per-capacitor voltage split: When V_total is positive, the voltage across each of the first four capacitors is shown. Smaller capacitance takes a larger share of the supply.

Two 47 uF caps in series with 12 V: enter C_1 = 47, C_2 = 47, unit = uF, V_total = 12. The capacitors in series calculator returns 23.5 uF equivalent and 6 V on each capacitor.

Once the equivalent capacitance is known, the capacitor charge calculator can turn that farad value into Q = C_eq x V_total for the combined capacitor and the charge it stores.

Putting the reciprocal-sum rule and the voltage split behind one form removes the busywork that distracts from circuit design.

• • Combine up to ten capacitors in one step: The form takes a chain of two to ten capacitors and reduces it to a single farad value, which is what most later circuit equations expect.
• • Skip the manual 1/C math: The reciprocal sum and its inverse are computed in one pass, so there is no risk of forgetting to invert the sum at the end.
• • Use any supported prefix as the form unit: The selector converts F, mF, uF, nF, and pF entries to farads before the formula runs. Mixed-prefix strings need conversion to one chosen unit first.
• • Read the per-capacitor voltage split: Voltage divider outputs show how the supply voltage lands on each capacitor, which is the practical answer when capacitors are wired as a divider.
• • Use the smallest capacitance as a sanity check: The calculator shows the smallest active capacitance so the user can confirm that the equivalent is in fact smaller, matching the same-charge rule.
• • Pick the right display unit automatically: Equivalent C and smallest C are rendered in the unit that fits the magnitude, so 1.86e-7 F is read directly as 186.3 nF without manual prefix work.

Once the equivalent series capacitance is known, the electrical resistance calculator is the natural follow-up when the next step is to combine a resistor with the equivalent C in an RC timing check.

The reciprocal-sum rule is exact for ideal capacitors. Real components add tolerances and parasitic effects that move the answer away from the textbook number.

• • The calculator assumes ideal capacitors with stable capacitance across the operating voltage. Class-2 ceramics and polymer capacitors drift with bias and temperature, so the answer is a first-pass estimate.
• • The voltage split uses the same-charge rule and assumes DC equilibrium. AC operation adds reactance and phase shift that the series RC model does not capture.
• • The per-capacitor voltage outputs only cover the first four capacitors. Strings longer than four require manual extension using V_i = V_total x C_eq / C_i.

When leakage current or ESR is non-negligible, the Ohm's law calculator helps quantify the small leakage resistor that sits in parallel with each capacitor and shapes the DC bias on the string.