Capacitor Calculator
Capacitor Calculator
Combine capacitors in series or parallel with the voltage split, find RC charge and discharge times, energy and charge stored, reactance and filter cutoff, and read capacitor codes such as 104 or 473K in both directions.
Series and parallel totals
Series: 1 ÷ Ct = 1 ÷ C1 + 1 ÷ C2 + and so on. Parallel: Ct = C1 + C2 + and so on. Charge Q = C × V and energy E = ½ × C × V². Time constant τ = R × C, with the voltage rising as 1 − e to the power (−t ÷ τ) and falling as e to the power (−t ÷ τ). Reactance Xc = 1 ÷ (2π × f × C) and the RC cutoff fc = 1 ÷ (2π × R × C). Codes follow IEC 60062 and maker tables. The calculator models an ideal capacitor, with no tolerance, ESR, leakage or voltage effects. The CSV, image and printed report contain the values you entered, nothing preloaded.
How to use this tool
Choose what you want from the first box. "Combine capacitors" takes up to six values, each with its own unit box, and gives the total for series or parallel. "RC charge and discharge" takes a resistance, a capacitance and, if you want volts, a source voltage. "Energy and charge" works from capacitance and voltage, or backward from an energy. "Reactance and filter" gives reactance, the cutoff of an RC filter, or the capacitor needed for a cutoff. "Capacitor codes" reads a marking such as 104K or writes one for a value.
The input people most often get wrong is the unit box beside each number. 100 with µF selected is a thousand times bigger than 100 with nF selected, and that single slip turns a 100 nF bypass capacitor into a 100 µF electrolytic. Check the box before you trust the answer, and do the same for kHz against Hz and ms against s. The applied voltage in series mode is optional, but without it you get no voltage split.
What the calculation is doing
Capacitors in parallel share the same voltage and their capacitances add: Ct = C1 + C2 + and so on. Capacitors in series carry the same charge, and the reciprocals add: 1 ÷ Ct = 1 ÷ C1 + 1 ÷ C2 + and so on. Because the charge Q is common in a series chain, the voltage across each capacitor is Vi = Q ÷ Ci, and those voltages add up to the applied voltage.
For a resistor charging a capacitor from a source Vs, the capacitor voltage is Vs × (1 − e to the power −t ÷ τ), with τ = R × C. Discharging is Vs × e to the power −t ÷ τ. Solving for time gives t = −τ × ln(1 − p) to reach a fraction p while charging, and t = −τ × ln(p) to fall to p while discharging. Energy is E = ½ × C × V² and charge is Q = C × V, so V = √(2E ÷ C) and C = 2E ÷ V² when you work backward.
Reactance is Xc = 1 ÷ (2π × f × C), in ohms. An RC filter has its corner at fc = 1 ÷ (2π × R × C), where the reactance equals R and the gain is 1 ÷ √2, or 70.7%. A code XYZ is XY × 10 to the power Z picofarads, so the first two digits are the value and the third is the number of zeros. A zero capacitance, frequency or resistance gives a message instead of a number.
Why series capacitors behave like resistors in parallel
The rules look backward the first time you meet them. Resistors in series add and resistors in parallel take the reciprocal, but capacitors do the opposite. The reason is that capacitance grows with plate area and shrinks with the gap. Parallel capacitors add plate area, so their capacitances add. Series capacitors add gap, so the total goes down and can never beat the smallest part.
Series voltage shares out the other way from what most people guess. With 100 µF and 220 µF across 12 V, the same charge of 825 µC sits on both plates, and V = Q ÷ C puts 8.25 V across the 100 µF part and 3.75 V across the 220 µF part. The smaller capacitor takes the bigger share because it has the bigger reactance, just as the larger resistor does in a voltage divider. Two equal capacitors split the voltage in half, which is why two 10 µF parts make 5 µF and each carries half the supply.
That split is the AC picture, or the picture while the capacitors charge. In steady DC the leakage of each part matters. One design article on series capacitors notes that the part with the lowest leakage takes a disproportionately high share of the voltage, and that designers add balancing resistors across each capacitor for that reason. If you stack capacitors for a higher voltage rating on a DC supply, do not rely on the ideal split.
What the time constant tells you
The time constant is the one number that describes an RC circuit, and the percentages it produces do not depend on the values. After 1 τ a charging capacitor has 63.2% of the source voltage, after 2 τ 86.5%, and after 5 τ 99.3%, so 0.7% of the step is still to go. The rule of thumb that 5 τ means finished accepts a 0.7% error. For 99.9%, wait about 6.9 τ.
Two other times are worth remembering. The capacitor reaches half the source voltage after 0.693 τ, and 90% after 2.303 τ. With 10 kΩ and 100 µF, τ is 1 s, so 90% takes 2.303 s. The resistance in the formula is the total resistance the capacitor sees, so add the internal resistance of the source to any resistor you fit, or the real circuit will be slower than the calculation.
| Time constants | Charging reaches | Discharging leaves | Time for 10 kΩ and 100 µF | Volts from a 12 V source |
|---|---|---|---|---|
| 1 τ | 63.2% | 36.8% | 1 s | 7.585 V |
| 2 τ | 86.5% | 13.5% | 2 s | 10.38 V |
| 3 τ | 95.0% | 5.0% | 3 s | 11.4 V |
| 4 τ | 98.2% | 1.8% | 4 s | 11.78 V |
| 5 τ | 99.3% | 0.7% | 5 s | 11.92 V |
Energy goes with the square of the voltage
The energy in a capacitor is ½ × C × V², so voltage matters more than capacitance. A 100 µF capacitor at 5 V holds 1.25 mJ and at 10 V holds 5 mJ. Doubling the voltage quadruples the energy, and at half the voltage a capacitor holds a quarter. The derivation is short: the work of charging is the integral of V dQ with V = Q ÷ C, which is ½ × Q² ÷ C.
Working backward is useful for sizing. A defibrillator example in the OpenStax physics text delivers 400 J from a capacitor charged to 10,000 V, and C = 2E ÷ V² gives 8 µF. The tool solves that in one step. One more fact matters if you charge through a resistor: HyperPhysics points out that only half of the work done by the source ends up as energy in the capacitor, and the other half is lost as heat in the resistance, whatever its size.
Reactance and the corner of an RC filter
Reactance is the opposition a capacitor presents to alternating current, and it falls as the frequency rises. A 1 µF capacitor has 2.653 kΩ at 60 Hz. A 100 nF capacitor has 1.592 kΩ at 1 kHz and one tenth of that, 159.2 Ω, at 10 kHz. At zero frequency, which is DC, the reactance is infinite, so a capacitor blocks steady current and passes a changing one. Reactance is not resistance, because an ideal capacitor uses up no power.
| Capacitor | 50 Hz | 60 Hz | 1 kHz | 10 kHz | 100 kHz |
|---|---|---|---|---|---|
| 10 nF | 318 kΩ | 265 kΩ | 15.9 kΩ | 1.59 kΩ | 159 Ω |
| 100 nF | 31.8 kΩ | 26.5 kΩ | 1.59 kΩ | 159 Ω | 15.9 Ω |
| 1 µF | 3.18 kΩ | 2.65 kΩ | 159 Ω | 15.9 Ω | 1.59 Ω |
| 10 µF | 318 Ω | 265 Ω | 15.9 Ω | 1.59 Ω | 0.159 Ω |
| 100 µF | 31.8 Ω | 26.5 Ω | 1.59 Ω | 0.159 Ω | 0.0159 Ω |
Put a resistor in series and you have a filter. The corner frequency fc = 1 ÷ (2π × R × C) is where the reactance equals the resistance, the output is 70.7% of the input, and the level is down 3.01 dB, which is half the power. With 4.7 kΩ and 47 nF the corner is 720.5 Hz. Taking the output across the capacitor makes a low pass filter that falls by 20 dB for every tenfold rise above the corner, so at 10 kHz the gain is 0.0719, or −22.9 dB, and a 10 V input gives about 0.72 V. Taking it across the resistor makes a high pass filter, with the same corner.
Capacitor codes and tolerance letters
Small capacitors are marked with three digits and sometimes a letter. The first two digits are the value in picofarads and the third is the number of zeros, so 104 is 100,000 pF, which is 100 nF, and 473 is 47 nF. The third digit only runs from 0 to 7 in this tool. Some makers use 8 and 9 for multipliers of 0.01 and 0.1, but the sources disagree, so the tool asks you to write values below 10 pF with an R for the decimal point, such as 4R7 for 4.7 pF. Another notation puts the unit letter where the decimal point would be, so 4n7 is 4.7 nF.
| Code | Working | Picofarads | Reads as |
|---|---|---|---|
| 220 | 22 × 10⁰ | 22 | 22 pF |
| 101 | 10 × 10¹ | 100 | 100 pF |
| 471 | 47 × 10¹ | 470 | 470 pF |
| 102 | 10 × 10² | 1,000 | 1 nF |
| 472 | 47 × 10² | 4,700 | 4.7 nF |
| 103 | 10 × 10³ | 10,000 | 10 nF |
| 473 | 47 × 10³ | 47,000 | 47 nF |
| 104 | 10 × 10⁴ | 100,000 | 100 nF |
| 224 | 22 × 10⁴ | 220,000 | 220 nF |
| 474 | 47 × 10⁴ | 470,000 | 470 nF |
| 105 | 10 × 10⁵ | 1,000,000 | 1 µF |
| 106 | 10 × 10⁶ | 10,000,000 | 10 µF |
The letter after the digits is the tolerance. J, K and M are ±5%, ±10% and ±20% on nearly every chart. B, C and D are fixed steps of ±0.1, ±0.25 and ±0.5 pF in the Murata and Vishay tables, which suits small values. F and G are ±1% and ±2% above about 10 pF, and Wikipedia gives them as 1 pF and 2 pF for the smallest parts. S is +50% and −20%, and Z is +80% and −20%. The letter H shows up as ±3% in some tables and is missing from others, so the tool does not decode it.
| Letter | Tolerance | Kind | Range on 100 nF |
|---|---|---|---|
| B | ±0.1 pF | small values, fixed steps in pF | about 100 nF |
| C | ±0.25 pF | small values, fixed steps in pF | about 100 nF |
| D | ±0.5 pF | small values, fixed steps in pF | about 100 nF |
| F | ±1% | percent | 99 nF to 101 nF |
| G | ±2% | percent | 98 nF to 102 nF |
| J | ±5% | percent | 95 nF to 105 nF |
| K | ±10% | percent | 90 nF to 110 nF |
| M | ±20% | percent | 80 nF to 120 nF |
| S | +50% and −20% | asymmetric percent | 80 nF to 150 nF |
| Z | +80% and −20% | asymmetric percent | 80 nF to 180 nF |
Real capacitors are not ideal
The calculator models an ideal capacitor, so it has no tolerance, leakage, series resistance or voltage effects. Real parts add several. The tolerance letter sets how far the value can be off. Voltage rating is a hard limit that designers derate. Equivalent series resistance and leakage shape behavior at high frequency and at DC, and dielectric absorption lets a discharged capacitor creep back up in voltage.
Ceramic capacitors have one more effect that surprises people. In the class 2 types, such as X5R and Y5V, the capacitance drops as DC voltage is applied. Murata gives an example in which an X5R part loses about 10% and a Y5V part about 40% at 1.8 V DC, while the temperature compensating C0G parts show almost no change. So a 10 µF ceramic capacitor on a 5 V rail may give you well under 10 µF, and the tool cannot know that.
A worked example you can check on paper
The default view is 100 µF and 220 µF in series with 12 V applied. The reciprocals are 1 ÷ 100 = 0.01 and 1 ÷ 220 = 0.004545 per µF, which add to 0.014545, and 1 ÷ 0.014545 = 68.75 µF. The charge is 68.75 µF × 12 V = 825 µC, on each capacitor. Then 825 µC ÷ 100 µF = 8.25 V and 825 µC ÷ 220 µF = 3.75 V, which add to 12 V. The energy is ½ × 68.75 µF × 12² = 4.95 mJ. In parallel the same parts give 100 + 220 = 320 µF.
For the RC case, 10 kΩ × 100 µF = 1 s. After 1 s from a 12 V source the capacitor holds 12 × (1 − e to the power −1) = 12 × 0.6321 = 7.585 V. For the code case, 473K is 47 × 10³ pF = 47 nF, and K is ±10%, so the part lies between 47 × 0.9 = 42.3 nF and 47 × 1.1 = 51.7 nF.
Mistakes that catch people out
Mixing up nF and µF. A thousand times is a big miss, and it usually comes from the unit box. Read the unit beside the number, and check the code: 104 is 100 nF, never 104 pF, and never 100 µF.
Reading 220 as 220 pF. The third digit is a count of zeros, so 220 is 22 with no zeros added, which is 22 pF. A 220 pF part is marked 221.
Expecting a series total above the smallest part. It cannot happen. If the series answer is larger than one of your capacitors, a unit is wrong or you meant parallel. The check is quick: the series total must be under the smallest capacitor and the parallel total above the largest.
Treating 5 τ as exact. The capacitor never quite finishes, and 0.7% is still left at 5 τ. Also count every resistance in the loop, including the source, or the real circuit lags the answer.
Trusting the ideal voltage split on DC. The split follows capacitance while charging, but leakage decides it in the long run. Use balancing resistors, and rate each capacitor for its share.
Popular calculations
Each link opens the calculator with those figures filled in.
Combine capacitors in series or parallel
RC time constant, charge and discharge
Energy and charge stored
Reactance and RC filter cutoff
Capacitor codes
How this was checked
The formulas were compared with OpenStax University Physics Volume 2 (chapters 8 and 10), HyperPhysics, Wikipedia pages on capacitors, RC circuits, low pass filters and ceramic capacitors, and the Electronics Tutorials passive filter page. The engine reproduces the OpenStax examples: 0.755 µF for 1, 5 and 8 µF in series (0.7547 exactly), 14 µF in parallel, 4.0 µF with 4.0 V and 8.0 V for the 12 V network, and 8 µF for the defibrillator. The Electronics Tutorials filter, 4.7 kΩ and 47 nF, gives 720.5 Hz against the 720 Hz they print.
Independent routes were used as well. An RK4 integration of the RC equation matched the closed form at 1 to 5 τ within 3.4e−15 of the source voltage, and matched the time to reach a level in 60 random cases within 8e−9 τ. Series totals and voltages matched an exact fraction based nodal solve of 300 random chains of two to six capacitors, within 4.1e−16. Energy from numerically integrating V dQ matched ½CV² in 200 cases within 2e−14. Reactance from a differentiated sine wave, and filter gain and phase from the complex impedance divider, agreed. All 720 three digit codes, all 180 R codes and 400 random RKM values made the round trip from code to value and back, and the tolerance letters match the Murata and Vishay tables and Wikipedia.
Common questions
How do you find the total capacitance of capacitors in series and in parallel?
In parallel the capacitances simply add, so 100 µF and 220 µF give 320 µF. In series you add the reciprocals, 1 ÷ Ct = 1 ÷ C1 + 1 ÷ C2, which for the same two parts gives 68.75 µF. The series total is always smaller than the smallest capacitor, and two equal capacitors in series give half of one, so two 10 µF parts make 5 µF. The tool handles up to six capacitors and any mix of pF, nF, µF, mF and F.
What does the time constant of an RC circuit mean?
The time constant τ is R times C, in seconds when R is in ohms and C is in farads. After one τ a charging capacitor has covered 63.2% of the distance to the source voltage, and a discharging one has 36.8% left. After 5 τ about 0.7% of the step remains, which is why 5 τ is the usual rule of thumb for calling a charge finished. With 10 kΩ and 100 µF, τ is 1 s.
How do you read a capacitor code such as 104 or 473K?
The first two digits are the value and the third is the number of zeros to add, in picofarads. So 104 is 10 followed by 4 zeros, which is 100,000 pF or 100 nF, and 473 is 47,000 pF or 47 nF. A code such as 220 is 22 pF, not 220 pF, because the third digit is zero. A letter after the digits is the tolerance, so 473K is 47 nF at ±10%.
How much energy does a capacitor store?
E = ½ × C × V², with C in farads and V in volts giving joules. A 100 µF capacitor at 5 V stores 1.25 mJ and at 10 V stores 5 mJ, four times as much for twice the voltage. The charge is Q = C × V, so the same 100 µF capacitor at 5 V holds 500 µC.
Why does a capacitor block DC but pass AC?
The reactance Xc = 1 ÷ (2π × f × C) grows without limit as the frequency falls toward zero, so a charged capacitor passes no steady DC current. As the frequency rises the reactance drops. A 1 µF capacitor has 2.653 kΩ at 60 Hz and about a tenth of that at 600 Hz.
What is the cutoff frequency of an RC filter?
fc = 1 ÷ (2π × R × C). At that frequency the reactance of the capacitor equals R, the output is 70.7% of the input, which is −3 dB, and half the power gets through. A 4.7 kΩ resistor with a 47 nF capacitor gives 720.5 Hz. Above the cutoff a low pass filter falls by 20 dB for every tenfold rise in frequency.
Related Calculators and Reference
- Ohm Law Calculator: voltage, current, resistance and power, the DC side of any RC circuit you are sizing.
- Voltage Divider Calculator: the resistor version of the voltage split that series capacitors follow.
- LED Resistor Calculator: pick the series resistor for an LED before you add a smoothing capacitor to the supply.
- Resistor Color Code Calculator: read the resistor that sets your RC time constant or filter corner.
- Energy Converter: turn the joules stored in a capacitor into watt hours and other units.
- Complex Number Calculator: reactance and series or parallel impedance written with j.
- OpenStax University Physics Volume 2, section 8.2: the textbook derivation of series and parallel capacitor networks.