🔧 Capacitor Values
📐 Circuit Diagram
⚙️ Formula
📋 Voltage Distribution
| Capacitor | Capacitance | Voltage Drop |
|---|
📊 Results
Voltage (V)
12V
Equivalent C
50.00µF
Total Charge
0.60mC
Equivalent Capacitance
Total Charge (Q = Ceq × V)
Stored Energy (E = ½CV²)
Capacitors in Series Calculator — Complete Guide to Series Capacitance
This capacitors in series calculator instantly finds the equivalent capacitance for up to 6 capacitors connected end-to-end in a single current path using the reciprocal formula 1/Ceq = 1/C1 + 1/C2 + … + 1/Cn. It also shows the voltage across each capacitor, the shared charge Q, and the total stored energy — with a live circuit diagram that updates in real time. Use it for capacitor voltage-rating checks, AC coupling design, LC resonator tuning, and any circuit where you need to achieve a lower-than-standard capacitance value.
Quick Reference: Series Capacitor Formulas
| Quantity | Formula | Notes |
|---|---|---|
| Equivalent Capacitance | 1/Ceq = 1/C1 + 1/C2 + … + 1/Cn | Always < smallest C |
| Two Capacitors (shortcut) | Ceq = (C1 × C2) / (C1 + C2) | Product over sum |
| n Equal Capacitors | Ceq = C / n | e.g., 3× 15µF → 5µF |
| Charge (same on all) | Q = Ceq × Vtotal | All caps share same Q |
| Voltage across Ci | Vi = Q / Ci | Smaller C → larger V |
| Stored Energy | E = ½ × Ceq × V² | Also Ei = ½ × Q² / Ci |
How to Use This Capacitors in Series Calculator
Enter the supply voltage, then set the capacitance value and unit (pF, nF, µF, mF, F) for each capacitor. Click + Add Capacitor to include up to 6 capacitors. The calculator instantly shows Ceq, total charge, stored energy, and the voltage across every individual capacitor — and the live circuit diagram updates automatically.
The Series Capacitor Formula Explained
When capacitors are wired in series, only one current path exists. Charge can only accumulate on the outermost plates — the inner plates must remain neutral because they are electrically isolated. As a result, every capacitor stores exactly the same charge Q regardless of its individual capacitance. Since Q = C × V, a smaller capacitor must have a larger voltage across it to store the same charge. The total "effort" to store charge — the equivalent capacitance — is found by adding the reciprocals:
The result is always less than the smallest individual capacitor. Adding more capacitors in series always reduces Ceq.
Product-Over-Sum Shortcut (Exactly Two Capacitors)
Example: 10 µF and 22 µF → (10 × 22) / (10 + 22) = 220 / 32 = 6.875 µF
Equal-Capacitors Shortcut
Example: Three 15 µF capacitors in series → 15 / 3 = 5 µF
Why Series Capacitance Decreases
Think of a capacitor as two plates separated by a gap. Connecting two capacitors in series is equivalent to placing four plates in a row — the inner two are isolated and don't help store charge, so the effective plate separation doubles while the plate area stays the same. Since C = ε × A / d, doubling d halves C. More capacitors in series means even greater effective separation and even lower capacitance — the exact opposite of series resistors, which simply add up.
Voltage Distribution in Series Capacitors
Because all capacitors share the same charge Q, the voltage across each one is Vi = Q / Ci. Smaller capacitors carry a proportionally higher voltage. This is critical for safety:
Then: V1 = Q / C1, V2 = Q / C2, …
Check: V1 + V2 + … = Vtotal ✓
Worked Examples
Example 1: Two Capacitors — Product-Over-Sum
Problem: 10 µF and 22 µF in series across 12 V. Find Ceq, Q, and voltages.
Ceq = (10 × 22) / (10 + 22) = 6.875 µF
Q = 6.875 × 12 = 82.5 µC
V1 = 82.5 / 10 = 8.25 V V2 = 82.5 / 22 = 3.75 V ✓ 8.25 + 3.75 = 12 V
Example 2: Three Equal Capacitors
Problem: Three 15 µF capacitors in series across 9 V.
Ceq = 15 / 3 = 5 µF
Q = 5 × 9 = 45 µC V each = 45 / 15 = 3 V ✓ (3 × 3 = 9 V)
Example 3: Voltage Rating Check
Problem: Two 100 V–rated capacitors — 100 µF and 220 µF — in series across 100 V. Are they safe?
Ceq = (100 × 220) / 320 = 68.75 µF Q = 68.75 × 100 = 6875 µC
V1 = 6875 / 100 = 68.75 V ✓ V2 = 6875 / 220 = 31.25 V ✓ Both safe.
Series vs Parallel Capacitors — Complete Comparison
| Capacitors in Series | Capacitors in Parallel | |
|---|---|---|
| Formula | 1/Ceq = Σ(1/Ci) | Ceq = ΣCi |
| Result vs individual caps | Always < smallest C | Always > largest C |
| Voltage across each cap | Divides (inversely with C) | Same on all |
| Charge on each cap | Same on all | Divides (proportional to C) |
| Analogous to resistors | Parallel resistors | Series resistors |
| Used for | Voltage sharing, LC tuning, AC coupling | Filtering, decoupling, energy storage |
Capacitance Units Reference
| Unit | Symbol | Value in Farads | Typical Use |
|---|---|---|---|
| Farad | F | 1 F | Supercapacitors, energy storage |
| Millifarad | mF | 10⁻³ F | Large filter/power caps |
| Microfarad | µF | 10⁻⁶ F | Electrolytic, film caps |
| Nanofarad | nF | 10⁻⁹ F | Ceramic and film caps |
| Picofarad | pF | 10⁻¹² F | RF, timing, parasitic caps |
Practical Applications of Series Capacitors
- Voltage rating increase: Two 100 V capacitors in series can withstand 200 V. Always add balancing resistors in parallel to compensate for leakage differences.
- AC coupling: Series capacitors block DC while passing AC signals between amplifier stages or speaker systems.
- LC resonator tuning: Series capacitors fine-tune the effective capacitance of an LC filter to achieve a precise resonant frequency.
- Achieving non-standard values: Combine standard E-series capacitors in series to hit a target value between catalogue sizes.
- Capacitive voltage dividers: Used in high-voltage measurement probes and power-line data coupling.
Common Mistakes to Avoid
- Result larger than the smallest cap: If your Ceq is bigger than any individual capacitor, you've used the parallel formula — check again.
- Mixing units: Convert everything to one unit (µF) before calculating, or use this calculator which handles unit conversion automatically.
- Ignoring voltage ratings: The voltage across each capacitor depends on relative capacitance — always verify no single capacitor exceeds its voltage rating.
- Unbalanced leakage in series stacks: For high-voltage series stacks add equalising resistors (typically 100 kΩ) across each capacitor so leakage differences don't push one cap above its rating.
Frequently Asked Questions
Why is series capacitance always less than the smallest capacitor?
Adding positive reciprocals always gives a sum whose reciprocal is smaller than any single term. Physically, the weakest (smallest) capacitor limits the total stored charge per volt of the whole chain.
Can I mix different capacitor types in series?
Yes, but exercise caution. Different types have different leakage currents, ESR, and voltage characteristics. Add balancing resistors across electrolytics to equalise DC voltage distribution.
How do I use series capacitors to hit a specific target value?
For two capacitors, rearrange the product-over-sum formula: given Ctarget and C1, find C2 = (Ctarget × C1) / (C1 − Ctarget). Experiment with values using this calculator.
Related Calculators
- Capacitors in Parallel Calculator — Ceq = C1 + C2 + C3
- Parallel Resistor Calculator — same reciprocal formula as series capacitors
- Series Resistor Calculator
- RLC Series Resonance Calculator — uses series capacitors
- Inductors in Series Calculator
- Ohm's Law Calculator