Electrical Formula Reference & Calculator

Ohms Law Wheel for Voltage, Current, Resistance & Power

The Ohms Law Wheel puts all twelve V-I-R-P equations in one place. Enter any two values in the wheel calculator and get voltage, current, resistance and power with the exact formula shown. Or open one of twelve free electrical calculators.

  • 12 Core Formulas
  • 12 Electrical Calculators
  • Instant Browser Calculations
VIRP ΩAWV Resistance Current flow Ω V · I · R · P
Flagship tool

Interactive Ohms Law Wheel Calculator

Two known quantities are enough. The solver normalises everything to SI base units, applies the correct equation from the wheel, and shows the substitution it used.

V = I × RV = P ÷ IV = √(P × R)VI = V ÷ RI = P ÷ VI = √(P ÷ R)IP = V × IP = I² × RP = V² ÷ RPR = V ÷ IR = V² ÷ PR = P ÷ I²R Ω

Select a quadrant. The wheel highlights the three formulas that solve for that quantity and marks the matching input in the solver beside it.

V-I-R-P Solver

Fill in any two boxes and leave the other two blank.

Enter 2 more values (two are needed).

Twelve tools, five categories

Electrical Calculators Built Around the Ohms Law Wheel

The wheel solves V-I-R-P. These twelve tools take it further — resistor networks, conductor drop, LED current limiting, 555 timing and running costs. Filter by category, then open any tool for the working, a worked example and the limits of its model.

Getting started

How to Use the Ohms Law Wheel

Six short steps take you from two measured values to a full, checked picture of the circuit.

Choose Two Known Values

Decide which two of voltage, current, resistance and power you already know from a datasheet, a meter reading or the circuit design.

Enter Values and Set Units

Type each figure into its box and pick the matching unit. Milliamps, kilohms and microvolts are all handled without manual conversion.

Run the Calculation

Select Calculate. The wheel picks the equation that matches your pair of inputs and solves for the two remaining quantities.

Review the Formula and Result

Check the substituted equation beneath each result so you can follow the arithmetic, then copy the whole summary if you need it elsewhere.

Check the Component Ratings

Compare the power figure against what your parts can dissipate. A 0.25 W resistor asked to carry 1 W will fail, so leave roughly a two-to-one margin before you order.

Take It to a Dedicated Tool

Reduce a network first, then apply the wheel. The series, parallel and voltage drop calculators handle the step before the wheel.

What it does

Built for Real Electrical Work

The wheel is the centre of the site, and every design decision supports getting a trustworthy number quickly.

Complete V-I-R-P Wheel

All twelve equations are implemented, including the square-root forms that most quick calculators leave out.

Any Two Values

Voltage and power, resistance and power, current and resistance: every valid pair is solved by the same engine.

Automatic Unit Conversion

Microvolts through kilovolts, milliohms through megohms. Conversion to SI happens before arithmetic, never after.

Formula Breakdown

Each answer carries the equation used and the substituted version with your own numbers in place.

Responsive Calculator

The same layout works on a workshop phone, a tablet on a bench and a wide desktop monitor.

Browser-based Calculation

Every result is computed locally in JavaScript. Your figures are never transmitted, because nothing is sent to a server.

Complete reference

The Twelve Ohms Law Wheel Formulas

Four target quantities, three routes to each. The group you need depends entirely on which two values you already have — plus the two supporting groups every real circuit ends up needing.

Calculate Voltage

  • V = I × R
  • V = P ÷ I
  • V = √(P × R)

Use the first form when you know the current and resistance, the second when a device is rated in watts at a known current, and the third when only power and resistance are on the label.

Calculate Current

  • I = V ÷ R
  • I = P ÷ V
  • I = √(P ÷ R)

The second form is the everyday one for appliances: a 1200 W device on a 120 V supply draws 10 A, which is what decides the circuit breaker and the conductor size.

Calculate Resistance

  • R = V ÷ I
  • R = V² ÷ P
  • R = P ÷ I²

R = V² ÷ P is how you work backwards from a heating element's rating to its cold resistance estimate, which you can then check with a multimeter.

Calculate Power

  • P = V × I
  • P = I² × R
  • P = V² ÷ R

P = I² × R is the form that explains conductor heating and resistor ratings, because doubling the current quadruples the heat produced.

Combine Resistances

  • R total = R₁ + R₂ + …
  • 1 ÷ R total = 1÷R₁ + 1÷R₂
  • Vout = Vin × R₂ ÷ (R₁ + R₂)

The wheel works on one resistance at a time, so reduce the network first. Use the series, parallel and divider calculators, then bring the equivalent value back to the Ohms Law Wheel.

Energy and Cost

  • E = P × t
  • kWh = (W × h) ÷ 1000
  • Cost = kWh × tariff

Power is the bridge from the wheel to a bill. Once P is known, hours of use and your tariff give the running cost — which is exactly what the electricity calculator works out.

Where the Ohms Law Wheel Comes From

Georg Ohm published the relationship between potential difference, current and resistance in 1827, after measuring how the current through different lengths of wire changed as he varied the driving voltage. His result, that current is proportional to voltage and inversely proportional to resistance, is the single equation most people remember as Ohms Law: I = V ÷ R.

Power arrived from a different direction. James Prescott Joule showed that the heat produced in a conductor is proportional to the square of the current and to the resistance, which gives P = I² × R and, more generally, P = V × I. The Ohms Law Wheel is what you get when you take those two laws and algebraically substitute one into the other in every valid combination. Nothing new is added; the wheel simply saves you from rearranging equations under time pressure.

That is why the wheel has twelve entries rather than four. Each quantity can be reached from three different pairs of inputs, and choosing the right one depends on what your meter, datasheet or nameplate actually tells you.

Reading a Value from the Wheel

Start from what you know. If you measured 12 V across a resistor and 2 A through it, you are in the voltage-and-current pair, so resistance comes from R = V ÷ I and power from P = V × I. If instead a heating element is marked 1500 W at 230 V, you have power and voltage, so current comes from I = P ÷ V and resistance from R = V² ÷ P.

The square-root forms catch people out because they appear less often in textbooks. They exist for the case where you know power and resistance but neither voltage nor current: V = √(P × R) and I = √(P ÷ R). A 25 W resistor rated at 100 Ω will therefore see 50 V across it and 0.5 A through it at full dissipation.

Select any quadrant on the interactive wheel above and the solver marks the matching input, so you can see which equation is about to be used before you calculate.

Units and Measurement

Volts, amperes, ohms and watts are the SI units behind the wheel, and the calculator converts every entry into those base units before doing arithmetic. This matters more than it sounds: a great many circuit mistakes come from mixing milliamps with amps or kilohms with ohms halfway through a calculation. Entering 20 mA and 470 Ω directly, and letting the tool normalise them, removes that class of error.

In practice you obtain these values with a multimeter. Voltage is measured across a component with the meter in parallel; current is measured by breaking the circuit and putting the meter in series; resistance is measured with the component isolated and the circuit de-energised. Power is almost never measured directly at hobby level, which is precisely why the power equations in the wheel are so useful.

Series and Parallel Behaviour

The wheel describes a single resistive element or an equivalent resistance, so combining components comes first. In a series circuit the same current passes through every component and the individual voltage drops add up to the supply voltage, with a total resistance of R₁ + R₂ + …. In a parallel circuit each branch sees the same voltage and the branch currents add, with the reciprocal of the total resistance equal to the sum of the reciprocals of the branches.

Once you have reduced a network to one equivalent resistance, every equation on the wheel applies to it directly. That is the workflow the calculators here are arranged around: reduce with the series or parallel resistor calculator, then apply the Ohms Law Wheel.

In the field

Understanding V-I-R-P in Practical Circuits

The same four quantities explain a dimmed LED, a warm extension lead and a tripping breaker.

Sizing a Current-Limiting Resistor

An LED is not a resistor. Its forward voltage stays roughly constant while its current rises steeply with small voltage increases, so it needs something in series to set the operating current. Subtract the forward voltage from the supply, and the remainder appears across the resistor. Ohms Law then gives the resistance, and P = I² × R gives the heat that resistor must handle. A 5 V supply with a 2 V LED at 20 mA needs 150 Ω dissipating only 60 mW, so a common 0.25 W part is comfortable — the LED resistor calculator does this for a whole string.

Why Conductors Get Warm

Every metre of cable has resistance, and P = I² × R says the heat produced rises with the square of the current. Doubling the load on an undersized extension lead does not double the heating; it quadruples it. The same resistance also produces a voltage drop along the run, which is why a motor at the far end of a long cable can start sluggishly even though the supply at the panel measures correctly. Estimate that drop with the voltage drop calculator.

Choosing a Resistor Power Rating

Resistor values are only half the specification. A 100 Ω resistor carrying 100 mA dissipates 1 W, which will destroy a typical quarter-watt part within seconds. Working out P = I² × R before ordering components, and then leaving a margin of roughly two to one, is the difference between a board that runs cool and one that discolours.

Estimating Running Costs

Power connects the electrical world to the billing world. Multiply watts by hours to get watt-hours, divide by a thousand for kilowatt-hours, and multiply by your tariff for the cost. A 1000 W appliance running for one hour uses exactly 1 kWh. Because P = V × I, you can start from a nameplate current instead of a wattage when that is all you have — then hand the figure to the electricity calculator.

Where the Simple Model Stops

Ohms Law assumes a linear, constant resistance. Real components drift from that assumption in ways worth knowing. A tungsten filament measures a few ohms cold and many times more when glowing, so switch-on current is far higher than steady-state current. Semiconductors are non-linear by design. In AC circuits, motors and transformers add inductive reactance, capacitors add capacitive reactance, and real power then depends on the power factor as well as on volts and amps.

Working Safely

Calculations are a design aid, not a substitute for safe practice. Isolate and verify before touching a circuit, treat every mains conductor as live until proven otherwise, and remember that conductor sizing in a real installation is governed by ampacity, grouping, ambient temperature and local code rules rather than by voltage drop alone. Where an installation is involved, have the design checked by a qualified electrician.

Electrical safety. The tools on this site give engineering estimates for study, prototyping and planning. They do not replace local electrical codes, manufacturer data, ampacity tables or a licensed electrician's assessment. Do not work on energised circuits.

Feedback

How People Use This Reference

Twelve short notes from the kinds of readers the site is written for.

I keep this open on a second monitor while I bench-test power supplies. Entering two values and getting the other two with the working shown saves me from second-guessing my own arithmetic.

Marcus Bell
United States

The wheel finally made the square-root forms click for me. Seeing V = √(P × R) written out with my own numbers substituted is what my textbook never did.

Priya Nair
India

The voltage drop tool is a quick sanity check before I size a run properly. I like that it says plainly it is not a substitute for the regulations.

Tom Whitfield
United Kingdom

Unit selectors are the detail that matters. Being able to type 20 mA instead of 0.02 removes the decimal-point mistakes I used to make.

Sarah Lindqvist
Canada

Clean, fast, no clutter. The resistor colour code page redraws the bands as I change each dropdown, which is far easier than reading a printed chart.

Daniel Kruger
Germany

I teach a first-year electronics module and point students here for the formula wheel. The layout of the twelve equations by target quantity is genuinely well thought out.

Camille Roux
France

The electricity calculator lets me set my own currency and tariff, so the cost figures actually mean something locally.

Ahmed Raza
Pakistan

Works properly on my phone in the workshop. Nothing overflows and the buttons are big enough to hit with gloves on.

Nurul Hidayat
Indonesia

The 555 astable page gives frequency and duty cycle together with the waveform, which is exactly what I need when I am prototyping.

Wei Lim
Malaysia

I appreciate that the LED calculator warns you when the supply voltage is below the string forward voltage instead of printing a nonsense resistor value.

Jessica Hartley
Australia

Loads instantly and everything is calculated in the browser, so I can use it on site where the signal is unreliable.

Omar Al Farsi
United Arab Emirates

The parallel resistor tool handling a zero-ohm branch gracefully instead of showing infinity is a small thing that shows care.

Grace Tan
Singapore

These are demonstration entries supplied with the template, not verified customer testimonials. Replace them with genuine, attributable feedback before publishing this site.

Twelve questions

Frequently Asked Questions

Split into the theory behind the wheel and the practical use of the calculators.

Ohms Law Wheel & Formulas

What is an Ohms Law Wheel?

An Ohms Law Wheel is a circular reference chart that arranges the relationships between voltage, current, resistance and power into four groups of three equations. The centre of the wheel holds the quantity you want to find, and the surrounding segment lists every formula that produces it from a different pair of known values. It combines Ohms Law with Joule's power law in a single diagram, which is why it covers twelve equations rather than the three most people memorise.

How many formulas are in the V-I-R-P wheel?

There are twelve: three for voltage, three for current, three for resistance and three for power. Each group of three exists because any of the remaining quantities can pair up in three different ways. For example, voltage can be found from current and resistance, from power and current, or from power and resistance.

What do V, I, R and P mean?

V is voltage, measured in volts, and represents the electrical pressure pushing charge through a circuit. I is current, measured in amperes, and represents the rate of charge flow. R is resistance, measured in ohms, and represents how much the material opposes that flow. P is power, measured in watts, and represents the rate at which electrical energy is converted into heat, light or motion.

How is Ohms Law related to electrical power?

Ohms Law on its own connects only voltage, current and resistance. Power comes from Joule's Law, P = V × I. Because Ohms Law lets you replace V with I × R or replace I with V ÷ R, you can rewrite the power equation as P = I² × R or P = V² ÷ R. Merging the two laws is exactly what produces the full wheel.

Can the wheel calculate any unknown value?

It can solve for the two unknowns whenever you supply any two of the four quantities, provided the pair you enter does not create a division by zero. Entering a current of zero and asking for resistance, for instance, has no defined answer. The calculator on this page checks for those cases and explains the problem rather than showing an error value.

When does basic Ohms Law not fully describe a circuit?

Ohms Law describes linear resistive behaviour. It does not describe semiconductors such as diodes and transistors, whose resistance changes with the applied voltage, and it does not account for reactance in AC circuits containing capacitance or inductance. It also assumes a constant temperature, while real conductors and filaments change resistance as they heat up.

Electrical Calculators & Practical Use

Which values do I need before I can calculate?

Two of the four. The calculator watches how many boxes are filled and tells you whether you need to add or clear a value. If you enter three, it asks you to remove one, because a third value would either be redundant or contradict the other two.

Are unit conversions supported?

Yes. Every numeric field has a unit selector covering the practical range, from microvolts to kilovolts and from milliohms to megohms. Values are converted to SI base units before any arithmetic happens, and results are then presented in the unit you selected alongside a readable engineering equivalent.

Can I use these calculators on a phone?

Every page is built to work from a 320-pixel-wide screen upward. Input fields, unit selectors and result panels reflow into a single column, and nothing scrolls sideways. Touch targets are sized so they can be used comfortably on site.

Do the calculators work offline once the page has loaded?

All arithmetic runs in JavaScript inside your browser, so once a page has finished loading it will keep calculating without a network connection. Nothing you type is sent anywhere, because there is no server-side calculation step at all.

Are these calculations suitable for AC circuits?

They apply directly to DC circuits and to purely resistive AC loads such as heaters and incandescent lamps, where you can use RMS values. For loads containing motors, transformers, capacitors or electronic drivers, you also need impedance and power factor, which these simplified tools do not model.

Should results replace professional electrical design?

No. Treat every figure as an engineering estimate for study, prototyping and planning. Real installations must follow local electrical codes, manufacturer specifications and ampacity rules, and any work on mains circuits should be designed and verified by a qualified electrician.

Put Two Values in and Let the Wheel Do the Rest

Voltage, current, resistance and power are four views of the same circuit. Start with the two you know.