Ohms Law Calculator
Free Ohms Law Calculator. Free online tool with accurate results using verified formulas. Includes worked examples, FAQ, and instant calculations.
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Ohm's Law states that voltage equals current times resistance (V = IR). Combined with the power formula (P = VI), any two known electrical values can determine the other two. This calculator uses all 12 derived formulas from the Ohm's Law power wheel.
Last reviewed: December 2025
Worked Examples
Example 1: LED Circuit Design
Example 2: Household Circuit
Background & Theory
The Ohm's Law Calculator — Voltage, Current, Resistance, Power 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 = kg·m/s²). 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 + ½at², v² = u² + 2as, and s = ½(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 = ½mv², where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g ≈ 9.81 m/s² 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 = ΔKE. 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 = I²R = V²/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength λ through f = v/λ, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/m²). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(mol·K), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gm₁m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant.
History
The history behind the Ohm's Law Calculator — Voltage, Current, Resistance, Power traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384–322 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 (1564–1642) 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 = mc². 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 Schrödinger, 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
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy
Ohms Law Calculator Formula
V = I × R | P = V × I | P = I²R | P = V²/R
Ohm's Law states that voltage equals current times resistance (V = IR). Combined with the power formula (P = VI), any two known electrical values can determine the other two. This calculator uses all 12 derived formulas from the Ohm's Law power wheel.
Ohms Law Calculator — Worked Examples
Example 1: LED Circuit Design
Problem: Calculate the resistor needed for a blue LED (3.2V forward voltage, 20mA) on a 9V battery.
Solution: Known: V_supply = 9V, V_LED = 3.2V, I = 20mA = 0.02A\nVoltage across resistor: V_R = 9 - 3.2 = 5.8V\nR = V / I = 5.8 / 0.02 = 290Ω\nNearest standard: 300Ω\nPower: P = V × I = 5.8 × 0.02 = 0.116W → Use 1/4W resistor
Result: R = 300Ω (1/4W) | I = 19.3mA | P = 0.116W
Example 2: Household Circuit
Problem: A 120V circuit has a 15A breaker. What is the maximum load resistance and power?
Solution: V = 120V, I_max = 15A\nMinimum resistance: R = V / I = 120 / 15 = 8Ω\nMaximum power: P = V × I = 120 × 15 = 1,800W\n80% rule: Continuous load should not exceed 80% = 1,440W (12A)
Result: R_min = 8Ω | P_max = 1,800W | Continuous max = 1,440W
Ohms Law Calculator — Frequently Asked Questions
What is Ohm's Law?
Ohm's Law is the fundamental relationship in electrical circuits that relates voltage (V), current (I), and resistance (R). Discovered by Georg Simon Ohm in 1827, it states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance: V = I × R. This means doubling the voltage doubles the current (if resistance stays the same), and doubling the resistance halves the current (if voltage stays the same). Ohm's Law is the foundation of all electrical engineering and is used in everything from designing simple LED circuits to planning power distribution systems.
What are the formulas for Ohm's Law?
The three basic Ohm's Law formulas are: V = I × R (voltage equals current times resistance), I = V / R (current equals voltage divided by resistance), R = V / I (resistance equals voltage divided by current). Adding power (P) gives additional formulas: P = V × I, P = I² × R, P = V² / R. From these you can derive: V = P / I, V = √(P × R), I = P / V, I = √(P / R), R = V² / P, R = P / I². The Ohm's Law wheel (or power wheel) arranges all 12 formulas in a circle for easy reference. You need any two known values to calculate the other two.
What are volts, amps, ohms, and watts?
These are the four fundamental electrical units: Voltage (V, volts) is the electrical pressure or potential difference that pushes electrons through a circuit — like water pressure in a pipe. Current (I, amps/amperes) is the flow rate of electrons — like the flow rate of water. Resistance (R, ohms/Ω) opposes current flow — like a narrow section in a pipe. Power (P, watts) is the rate of energy consumption — like the work done by the water flow. A helpful analogy: voltage is the height of a waterfall, current is how much water flows, resistance is rocks blocking the flow, and power is the energy of the falling water.
What is the difference between AC and DC in Ohm's Law?
Ohm's Law (V = IR) applies directly to DC (direct current) circuits. For AC (alternating current), the relationship becomes more complex because AC circuits include reactive components (inductors and capacitors) that create impedance (Z) rather than simple resistance. The AC version is V = I × Z, where Z is impedance measured in ohms but includes both resistance and reactance. For purely resistive AC loads (like heaters), Ohm's Law works the same as DC. For circuits with capacitors or inductors, you must account for phase angles and use complex numbers. Power calculations in AC also differ: real power (W) = V × I × cos(φ), where φ is the phase angle.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
What inputs do I need to use Ohms Law Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.