Calculate capacitors in series and parallel, RC charge and discharge time constants, energy stored in capacitors, capacitive reactance at any frequency, and RC filter cutoff — all 5 modes with pF/nF/µF unit conversion and IEC 60384 verified formulas.
Capacitors in series: 1/Ctotal = 1/C1 + 1/C2 + ... (total is always less than smallest):
Capacitance valueEnter valid capacitance.
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Capacitance valueEnter valid capacitance.
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Leave blank if not neededEnter valid capacitance.
Optional
Optional
Optional
+ Add C3–C6
Capacitors in parallel: Ctotal = C1 + C2 + ... (total is always greater than largest):
Capacitance valueEnter valid capacitance.
Select unitSelect unit.
Capacitance valueEnter valid capacitance.
Select unitSelect unit.
Leave blank if not neededEnter valid capacitance.
Optional
Optional
Optional
+ Add C3–C6
Resistance in ohms (use K suffix mentally)Enter valid resistance.
Capacitance valueEnter valid capacitance.
Select capacitance unitSelect unit.
For voltage at time calculationsEnter valid voltage.
Select charging or dischargingSelect mode.
Capacitance valueEnter valid capacitance.
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Voltage across capacitorEnter valid voltage.
Capacitance valueEnter valid capacitance.
Select capacitance unitSelect unit.
Signal frequency in Hz (1kHz = 1000)Enter valid frequency.
Enter R for -3dB cutoff frequencyEnter valid resistance.
Result
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⚠️ Disclaimer: Results use standard IEC capacitor formulas. RC time constants assume ideal components. Real capacitors have ESR, ESL, and leakage that affect performance. Always verify with measurements in critical applications.
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📚 Sources & Methodology
All capacitor formulas verified against:
IEC 60384-1:2021 — Fixed capacitors for use in electronic equipment: marking, ratings, and test methods iec.ch
IEEE Std 315-1975 (Reaffirmed 1993) — Graphic symbols for electrical and electronics diagrams, capacitor circuit analysis standards.ieee.org
NIST Handbook of Mathematical Functions — Exponential functions used in RC charge/discharge calculations nist.gov
Capacitors combine opposite to resistors. In series, total capacitance decreases (like parallel resistors). In parallel, total capacitance increases (like series resistors). This is because capacitors in series share charge but divide voltage, while capacitors in parallel share voltage and add charge. Series capacitors are used to reduce capacitance and handle higher voltages. Parallel capacitors are used to increase capacitance and reduce equivalent series resistance (ESR).
Core Capacitor Formulas (IEC 60384)
Series: 1/Ctotal = 1/C1 + 1/C2 + ... (reciprocal sum)Parallel: Ctotal = C1 + C2 + C3 + ... (direct sum)RC Tau: tau = R x C (time constant in seconds)Charge: V(t) = Vs x (1 - e^(-t/RC)) (charging)Discharge: V(t) = V0 x e^(-t/RC) (discharging)Energy: E = 0.5 x C x V^2 (joules)Charge Q: Q = C x V (coulombs)Reactance: Xc = 1 / (2 x pi x f x C) (ohms)RC Filter: fc = 1 / (2 x pi x R x C) (Hz, -3dB point)
RC Time Constant Reference Table
Time (multiples of tau)
Charging Voltage (%)
Discharging Voltage (%)
Practical Meaning
0.5 × RC
39.3%
60.7%
Half time constant
1 × RC
63.2%
36.8%
One time constant
2 × RC
86.5%
13.5%
Two time constants
3 × RC
95.0%
5.0%
Practically charged
4 × RC
98.2%
1.8%
Nearly complete
5 × RC
99.3%
0.7%
Fully charged (engineering)
ln(2) × RC = 0.693RC
50%
50%
Half-voltage point
ln(10) × RC = 2.303RC
90%
10%
90% charged
Capacitor Types and Applications
Ceramic (MLCC): 1pF to 100µF, non-polarized, very low ESR and ESL, excellent for high-frequency decoupling (0.1µF on every IC power pin) and RF circuits. X5R and X7R dielectric types are stable over temperature. Electrolytic: 1µF to 100,000µF, polarized (observe +/- polarity!), used for power supply bulk filtering, high values at low cost. Aluminum electrolytic has finite life. Tantalum: 1µF to 2200µF, polarized, very low ESR, no polarity reversal ever (may fail explosively). Film: 1nF to 100µF, non-polarized, very stable, used in audio and precision timing circuits.
Capacitive Reactance — How Capacitors Behave with AC
A capacitor blocks DC (Xc = infinity at f=0) and passes AC with decreasing impedance as frequency increases. At the RC filter cutoff frequency fc, the capacitive reactance equals the series resistance (Xc = R), giving 45° phase shift and −3dB output. Above fc, the capacitor increasingly short-circuits the signal. Below fc, the capacitor's high impedance passes the signal.
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Decoupling rule of thumb: Place a 100nF ceramic capacitor as close as possible to every IC power pin. This provides a local charge reservoir for fast transients. The capacitor resonates with PCB inductance around 50–200 MHz, filtering switching noise. Add a larger 10µF bulk capacitor per board section for low-frequency supply stiffening. This two-capacitor strategy covers the full frequency range from audio to RF.
❓ Frequently Asked Questions
1/Ctotal = 1/C1 + 1/C2 + ... Series total is always less than smallest. Two equal capacitors in series: Ctotal = C/2. Example: 10uF and 20uF in series: 1/Ctotal = 0.1 + 0.05 = 0.15, Ctotal = 1/0.15 = 6.67uF. Use the Series tab above for up to 6 capacitors with mixed units (pF/nF/uF).
Ctotal = C1 + C2 + C3 + ... Simply add all values. Unlike series, parallel total is larger than any individual. Three 100nF capacitors in parallel = 300nF. Multiple capacitors in parallel also reduce total ESR. Use the Parallel tab above — it accepts mixed units and up to 6 capacitors.
RC time constant tau = R x C. At time t = tau (1RC), a charging capacitor reaches 63.2% of supply voltage. At 5RC it is 99.3% (fully charged for engineering purposes). Example: R=47K, C=10uF: tau = 47000 x 0.00001 = 0.47 seconds. Full charge at 5 x 0.47 = 2.35 seconds. Use RC tab above — enter R in ohms, C in your preferred unit.
E = 0.5 x C x V^2 in joules. A 470uF capacitor at 16V: E = 0.5 x 0.00047 x 256 = 0.060J = 60mJ. Energy scales with V^2 — doubling voltage stores 4x the energy. Camera flash capacitors: 120uF at 300V stores 5.4J (enough for a bright flash). Power banks use supercapacitors (1F at 2.7V stores 3.65J per cell).
Xc = 1/(2 x pi x f x C). At DC (f=0), Xc is infinite — capacitor blocks DC. At high frequencies Xc approaches zero. Example: 100nF at 1kHz: Xc = 1/(6.2832 x 1000 x 0.0000001) = 1592 ohms. At 10kHz: 159 ohms. At 100kHz: 15.9 ohms. Use the Reactance tab for instant calculation at any frequency.
fc = 1/(2 x pi x R x C). This is the -3dB point where output = 0.707 x input. Low-pass: R in series, C to ground. High-pass: C in series, R to ground. Example: R=10K, C=100nF: fc = 1/(6.2832 x 10000 x 0.0000001) = 159.2 Hz. For 1kHz cutoff at 10K: C = 1/(2 x pi x 10000 x 1000) = 15.9nF (use 15nF or 22nF).
1 farad (F) = 1 coulomb/volt. In practice: 1uF = 10^-6 F. 1nF = 10^-9 F. 1pF = 10^-12 F. 1uF = 1000nF = 1,000,000pF. Common values: RF bypass 10-100pF. General ceramic decoupling 0.1-10uF. Power supply bulk 10-10000uF electrolytic. Energy storage: supercapacitors 1-3000F.
3-digit ceramic codes give value in pF: first two digits + third as multiplier. 104 = 10 x 10^4 pF = 100,000pF = 100nF = 0.1uF. 473 = 47 x 10^3 = 47000pF = 47nF. 221 = 22 x 10^1 = 220pF. Single-digit 5 = 5pF. Electrolytic capacitors print value directly in uF. Tolerance: J=5%, K=10%, M=20%.
V(t) = V0 x e^(-t/RC). At t=RC: 36.8% remains. At t=5RC: 0.7% remains (considered discharged). Example: 1000uF at 12V through 100 ohms: RC = 100 x 0.001 = 0.1 second. At 0.1s: 12 x 0.368 = 4.4V. Fully discharged at ~0.5 seconds. Use the RC Time Constant tab — enter Vs as initial voltage for discharge calculations.
Ceramic (MLCC): non-polarized, 1pF-10uF typical, very low ESR, stable, used for high-frequency decoupling. Electrolytic: polarized (positive terminal must be at higher voltage), 1uF-100,000uF, moderate ESR, limited lifespan, used for bulk power supply filtering. Tantalum: polarized, 1uF-2200uF, very low ESR, never reverse polarity. Film: non-polarized, 1nF-100uF, very stable, used in audio and precision timing.
1uF = 1,000nF = 1,000,000pF. To convert up (to larger unit): divide by 1000. To convert down: multiply by 1000. Examples: 4700pF = 4.7nF = 0.0047uF. 47nF = 0.047uF = 47,000pF. 10uF = 10,000nF = 10,000,000pF. All calculator tabs above accept pF, nF, uF, or mF — select the unit from the dropdown next to each capacitance input.
Q = C x V in coulombs. A 100uF capacitor at 5V: Q = 0.0001 x 5 = 0.0005 C = 500 microcoulombs (uC). During charging, current I = C x dV/dt. During discharge through R, initial current I0 = V0/R, then decays exponentially I(t) = I0 x e^(-t/RC). Use the Energy and Charge tab to calculate both Q and E for any capacitor and voltage.