Capacitor Calculator
Free Capacitor Calculator for electricity. Enter variables to compute results with formulas and detailed steps. Get results you can export or share.
Calculator
Adjust values & calculateCapacitive Reactance (Xc)
Formula
For series connections, the reciprocal of total capacitance equals the sum of reciprocals of individual capacitances. For parallel connections, total capacitance is the sum of all individual capacitances. Energy stored: E = 0.5CV2. Charge: Q = CV.
Last reviewed: December 2025
Worked Examples
Example 1: Series Capacitor Combination
Example 2: Parallel Capacitor Combination
Background & Theory
The Capacitor Calculator applies the following established principles and formulas. Physics is the fundamental natural science concerned with matter, energy, and the interactions between them. Classical mechanics, founded on Newton's three laws of motion, provides the framework for analyzing the motion of objects. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: F = ma, where force equals mass times acceleration in SI units of newtons (N = kgยทm/sยฒ). The third law establishes that every action produces an equal and opposite reaction. Kinematics describes motion without reference to its causes. The four fundamental equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t: v = u + at, s = ut + ยฝatยฒ, vยฒ = uยฒ + 2as, and s = ยฝ(u + v)t. These assume constant acceleration and are foundational for solving projectile motion, free fall, and linear dynamics problems. Energy conservation underpins much of physics. Kinetic energy is KE = ยฝmvยฒ, where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g โ 9.81 m/sยฒ near Earth's surface and h is height in meters. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ฮKE. Electricity and circuits rely on Ohm's law: V = IR, where voltage V is in volts, current I in amperes, and resistance R in ohms. Electrical power is P = IV = IยฒR = Vยฒ/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength ฮป through f = v/ฮป, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/mยฒ). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(molยทK), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gmโmโ/rยฒ, where G = 6.674ร10โปยนยน Nยทmยฒ/kgยฒ is the gravitational constant.
History
The history behind the Capacitor Calculator traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384โ322 BCE) proposed that all matter consisted of four elements and that objects moved toward their natural place, with heavier objects falling faster than lighter ones. While largely incorrect, his systematic approach to explaining nature dominated Western thought for nearly 2,000 years. The Scientific Revolution overturned Aristotelian physics. Galileo Galilei (1564โ1642) performed groundbreaking experiments on inclined planes and falling bodies, demonstrating that all objects fall with the same acceleration regardless of mass, and established the principle of inertia. His use of mathematics to describe motion was revolutionary. Isaac Newton synthesized these developments in his landmark Principia Mathematica (1687), laying out the three laws of motion and the law of universal gravitation. Newton's framework unified terrestrial and celestial mechanics, explaining planetary orbits with the same equations governing a falling apple. His calculus provided the mathematical language for expressing rates of change. The 19th century brought two major theoretical achievements. James Clerk Maxwell formulated his equations of electromagnetism between 1861 and 1862, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves traveling at the speed of light. Thermodynamics was developed by Carnot, Clausius, and Kelvin, establishing the laws governing heat, work, and entropy. The 20th century produced two revolutions that fundamentally altered the classical picture. Albert Einstein published the special theory of relativity in 1905, showing that space and time are not absolute but relative to the observer, and that mass and energy are equivalent via E = mcยฒ. His general theory of relativity in 1915 reinterpreted gravity as the curvature of spacetime. Simultaneously, quantum mechanics emerged from the work of Planck, Bohr, Heisenberg, and Schrรถdinger, revealing that at atomic scales energy is quantized and particles exhibit wave-particle duality. These developments culminated in the Standard Model of particle physics, which describes all known fundamental particles and three of the four fundamental forces.
Frequently Asked Questions
Formula
Series: 1/Ct = 1/C1 + 1/C2 + ... | Parallel: Ct = C1 + C2 + ...
For series connections, the reciprocal of total capacitance equals the sum of reciprocals of individual capacitances. For parallel connections, total capacitance is the sum of all individual capacitances. Energy stored: E = 0.5CV2. Charge: Q = CV.
Worked Examples
Example 1: Series Capacitor Combination
Problem: Three capacitors of 100 uF, 220 uF, and 470 uF are connected in series across a 12V supply. Find the total capacitance and stored energy.
Solution: 1/Ctotal = 1/100 + 1/220 + 1/470\n1/Ctotal = 0.01 + 0.004545 + 0.002128\n1/Ctotal = 0.016673\nCtotal = 59.98 uF\n\nEnergy = 0.5 x 59.98e-6 x 12^2\nEnergy = 0.5 x 59.98e-6 x 144\nEnergy = 4.319 mJ
Result: Total Capacitance: 59.98 uF | Energy: 4.319 mJ | Charge: 719.7 uC
Example 2: Parallel Capacitor Combination
Problem: The same three capacitors (100 uF, 220 uF, 470 uF) are connected in parallel across 12V. Find total capacitance and stored energy.
Solution: Ctotal = 100 + 220 + 470 = 790 uF\n\nEnergy = 0.5 x 790e-6 x 12^2\nEnergy = 0.5 x 790e-6 x 144\nEnergy = 56.88 mJ\n\nCharge = 790e-6 x 12 = 9,480 uC
Result: Total Capacitance: 790 uF | Energy: 56.88 mJ | Charge: 9,480 uC
Frequently Asked Questions
What is a capacitor and how does it store energy?
A capacitor is a passive electronic component that stores electrical energy in an electric field between two conductive plates separated by a dielectric material. When voltage is applied across the plates, opposite charges accumulate on each plate, creating an electric field that stores energy. The amount of energy stored is given by the formula E = 0.5 times C times V squared, where C is the capacitance and V is the voltage. Capacitors can release their stored energy very quickly, which makes them useful for applications requiring rapid bursts of power such as camera flashes, defibrillators, and power supply filtering in electronic circuits.
What is the difference between series and parallel capacitor connections?
In a series connection, capacitors are connected end to end so the same charge flows through each one, and the total capacitance decreases according to the reciprocal formula: 1/Ctotal = 1/C1 + 1/C2 + 1/C3. In a parallel connection, capacitors share the same voltage across their terminals, and the total capacitance simply adds up: Ctotal = C1 + C2 + C3. This is the opposite behavior of resistors, where series resistances add and parallel resistances use the reciprocal formula. Series connections are used when higher voltage ratings are needed, while parallel connections increase the total storage capacity of the circuit.
How do you choose the right capacitor for a circuit?
Choosing the right capacitor involves considering several key parameters: capacitance value for the required energy storage or filtering, voltage rating that exceeds the maximum expected voltage by at least 20 percent for safety margin, temperature rating for the operating environment, and equivalent series resistance (ESR) for power applications. The dielectric type also matters significantly because it affects temperature stability, voltage coefficient, and frequency response. Ceramic capacitors work well for high-frequency decoupling, electrolytic capacitors suit bulk energy storage in power supplies, and film capacitors are preferred for audio and precision applications due to their low distortion and excellent stability.
What is the energy stored in a capacitor and how is it calculated?
The energy stored in a capacitor is calculated using the formula E = 0.5 times C times V squared, where C is the capacitance in farads and V is the voltage across the capacitor. This quadratic relationship with voltage means doubling the voltage quadruples the stored energy, while doubling the capacitance only doubles the stored energy. A typical 1000 uF capacitor charged to 50 volts stores 1.25 joules of energy. While this seems small compared to batteries, capacitors can deliver this energy in microseconds, producing enormous instantaneous power. Supercapacitors with capacitances of hundreds of farads can store enough energy to briefly power electronic devices.
What is the charge stored on a capacitor?
The charge stored on a capacitor is calculated using Q = C times V, where Q is charge in coulombs, C is capacitance in farads, and V is voltage in volts. This linear relationship means doubling either the capacitance or the voltage will double the stored charge. In a series circuit, each capacitor holds the same charge regardless of its individual capacitance value, because the same current flows through all components. In a parallel circuit, each capacitor can hold a different charge proportional to its capacitance, but all share the same voltage. The total charge in a parallel combination equals the sum of individual charges on each capacitor.
What are common capacitor failure modes and how to prevent them?
Capacitors can fail due to several mechanisms including overvoltage breakdown, excessive temperature, ripple current heating, and electrolyte drying in electrolytic types. Overvoltage causes dielectric breakdown, permanently damaging the insulating layer between plates. Electrolytic capacitors are particularly susceptible to aging because their liquid or polymer electrolyte gradually dries out, reducing capacitance and increasing ESR over time. To prevent failures, always derate voltage by at least 20 percent, ensure adequate ventilation for heat dissipation, use capacitors rated for the expected ripple current, and replace electrolytic capacitors in critical applications every 5 to 10 years as part of preventive maintenance.
References
Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy