Capacitors in Series
Calculate total equivalent capacitance of up to 10 capacitors in series using the reciprocal formula 1/C = 1/C₁ + 1/C₂ + ... + 1/Cₙ. Free online electronics calculator with interactive charts and step-by-step breakdowns for students, hobbyists, and engineers.
About This Calculator
The Capacitors in Series Calculator computes the total equivalent capacitance when two or more capacitors are connected end-to-end in a series circuit. In this configuration, the same charge flows through each capacitor while the voltage divides across them. This calculator is essential for electronics engineers, students studying circuit theory, hobbyists building circuits, and anyone designing RC filters, timing circuits, or power supply systems.
The calculation uses the reciprocal formula: 1/Ctotal = 1/C₁ + 1/C₂ + ... + 1/Cn. This means the total capacitance is always smaller than the smallest individual capacitor value. For example, two 10 µF capacitors in series give 5 µF total. You can add up to 10 capacitors and optionally input the applied voltage to compute stored energy (E = ½CV²) and total charge (Q = CV). The unit selector supports farad (F), millifarad (mF), microfarad (µF), nanofarad (nF), and picofarad (pF).
Regional Notes
Global: Capacitor values are universally standardized (EIA, IEC), and the series formula applies regardless of region. Voltage ratings and safety standards may vary — always use capacitors rated for at least 1.5× the expected voltage in your circuit.
India (IS 13586): Indian Standard IS 13586 governs capacitor ratings for electronics. Common values are in µF and pF ranges. Verify voltage derating for 230 V AC mains applications.
United States (UL 810): UL 810 specifies capacitor safety standards. US hobbyists often use EIA standard values (e.g., 10 µF, 22 µF, 47 µF). For 120 V AC circuits, ensure X-rated safety capacitors are used.
United Kingdom (BS EN 60384): BS EN 60384 is the harmonized European standard for fixed capacitors. UK circuits commonly use 50 V DC and 250 V AC rated capacitors. Always check voltage derating for 230 V mains applications.
Frequently Asked Questions
What is the formula for capacitors in series?
The reciprocal formula for capacitors in series is 1/C_total = 1/C₁ + 1/C₂ + ... + 1/Cₙ. The total equivalent capacitance is always less than the smallest individual capacitor value.
Why is total capacitance in series less than any individual capacitor?
In a series configuration, capacitors share the same charge but the voltage divides across them. Since capacitance C = Q/V, and the total voltage is the sum of individual voltages, the equivalent capacitance is lower than the smallest capacitor in the circuit.
How do you calculate voltage across each capacitor in series?
The voltage across each capacitor in series is V_n = (C_total / C_n) × V_total. Capacitors with smaller capacitance values will have higher voltage drops, while larger capacitors will have lower voltage drops.
Is the charge the same for all capacitors in series?
Yes, when capacitors are connected in series, each capacitor stores the same amount of charge Q. This is because the charge on one capacitor comes from the adjacent capacitor, and conservation of charge ensures all capacitors have equal charge.
How do capacitors in series differ from capacitors in parallel?
In series, total capacitance decreases and follows the reciprocal formula 1/C = 1/C₁ + 1/C₂ + ... similar to parallel resistors. In parallel, total capacitance adds directly: C = C₁ + C₂ + ..., similar to series resistors.
What is the unit of capacitance?
The SI unit of capacitance is the farad (F). Common sub-units include millifarad (mF, 10⁻³ F), microfarad (µF, 10⁻⁶ F), nanofarad (nF, 10⁻⁹ F), and picofarad (pF, 10⁻¹² F). This calculator supports all common units for convenience.
How do I calculate stored energy in series capacitors?
The total energy stored in series capacitors is E = ½ × C_total × V², where C_total is the equivalent series capacitance and V is the total applied voltage. Each capacitor stores energy proportional to its capacitance and the square of its individual voltage.