The Ohm's law calculator above solves the complete set of relationships between voltage, current, resistance and power. Any two of those four are enough to determine the other two, which gives twelve distinct formulas altogether. Rather than making you pick the right one, this page asks which pair you know and applies the correct algebra behind the scenes.
Arb Digital builds free tools that pick one job and finish it properly. This one covers direct current and purely resistive circuits, which is where Ohm's law applies cleanly. The boundary against the site's other electrical pages is worth stating: the resistance converter rescales an ohm value between units and derives nothing, while the electrical power calculator extends into single-phase and three-phase AC with a power factor. This page stays with the four-quantity DC set.
What This Ohm's Law Calculator Does
Ohm's law proper is a single statement: the current through a conductor is proportional to the voltage across it, with resistance as the constant of proportionality. Written as an equation that is V = IR. On its own it links three quantities. Combining it with the definition of electrical power, P = VI, brings in a fourth and produces the twelve-formula set often drawn as a power wheel.
The tool implements all six input pairs. Voltage and current is the direct measurement case. Voltage and resistance suits a known component on a known rail. Current and resistance is the form used for voltage drop along a cable. The three pairs involving power suit specifications, since components are frequently rated by wattage rather than by the quantity you actually need.
Each result also comes with the specific relationship used, printed under the headline figure. That matters more than it sounds, because the most common error in this area is not arithmetic but reaching for the wrong form — using P = V2/R when the voltage you have is the supply rather than the drop across the component in question.
How to Use It
- Select the pair you actually measured. Do not enter guessed values into the other two fields expecting them to be reconciled; they are simply ignored.
- Watch the units on current and resistance. Milliamperes and kilohms are the everyday units in electronics, and the selectors convert to amperes and ohms before any arithmetic happens.
- Use the voltage across the component, not the supply. In a series circuit, each component drops only part of the supply voltage, and using the whole supply in a per-component calculation overstates everything.
- Read the power figure as a heat figure. Every watt calculated here is a watt the component has to shed. The note below the grid suggests a minimum resistor rating with headroom.
- Set a run time if you want energy. Watts are a rate. Multiplying by hours turns them into watt-hours, which is the quantity an electricity meter records.
The Formula: All Twelve Relationships
Ohm's law is V = IR. OpenStax University Physics Volume 2, section 9.4 on Ohm's law, states that V = IR, where V is the voltage measured in volts across the object, I is the current measured in amperes through it, and R is the resistance in ohms. Rearranged, I = V/R and R = V/I.
Electrical power is P = VI. Substituting Ohm's law into it in both directions gives P = I2R and P = V2/R. From those, the remaining rearrangements follow: V = P/I, V = √(PR), I = P/V, I = √(P/R), R = V2/P and R = P/I2. That is the full twelve. All four quantities are coherent SI derived units, and the SI Brochure published by the BIPM defines the volt, ampere, ohm and watt within that system.
Work the default values. A component with 12 volts across it passing 500 milliamperes, which is 0.5 amperes, has a resistance of 12 ÷ 0.5 = 24 ohms and dissipates 12 × 0.5 = 6 watts. Check the other forms agree: I2R is 0.25 × 24 = 6, and V2/R is 144 ÷ 24 = 6. Over one hour that component consumes 6 watt-hours.
Ohm's Law Is Not a Law of Nature
This is the point most treatments skip, and it explains a great many confusing measurements. Ohm's law is an empirical description of how some materials behave, not a universal rule. A material is called ohmic if its resistance stays constant as voltage changes, which makes the current-voltage graph a straight line through the origin. Metals at constant temperature are close to ohmic. Plenty of things are not.
A diode is the obvious counter-example. Below its forward voltage almost no current flows; above it, current rises steeply for a tiny further increase in voltage. Dividing voltage by current at any single point still gives a number in ohms, but that number changes completely at the next point, so it is not a property of the device. This is exactly why an LED needs a series resistor to set its current rather than being connected directly, a calculation the LED resistor calculator handles in full.
Even ordinary resistors drift. Resistance rises with temperature in most metals, so a component that is dissipating serious power is not at the same resistance it had when cold. An incandescent lamp filament is the extreme case: its cold resistance can be roughly a tenth of its hot resistance, which is why such lamps draw a large inrush current at switch-on and why they usually fail at the moment they are switched on rather than during operation.
The Square Relationship Is What Bites
Voltage and current relate linearly through resistance, so intuition works reasonably well there. Power does not. Two of the four power formulas involve a square, and the consequences catch people out repeatedly.
For a fixed resistance, doubling the current quadruples the power. A resistor comfortably running at a quarter of a watt becomes a one-watt resistor if the current doubles, and a quarter-watt part will scorch. The same square appears in cable losses: halving the current in a run for the same delivered power cuts the resistive loss to a quarter, which is the entire reason transmission networks run at high voltage.
Running the other way, for a fixed resistance, halving the supply voltage quarters the power. A heating element designed for 240 volts and connected to 120 produces a quarter of its rated heat, not half. This trips people up when moving equipment between regions, and it is a different question from the transformer rating, which the electrical power calculator covers for AC supplies.
Sizing a Resistor for the Power It Will Dissipate
The wattage number on a resistor is not a target, it is a survival limit — the power the part can dissipate continuously in free air without exceeding its rated temperature. Running a resistor at its rated power is legitimate on paper and unwise in practice, because that rating assumes an ambient temperature and an airflow that a crowded board rarely provides.
The usual working rule is to choose a part rated for at least twice the calculated dissipation, and more where the resistor sits near other hot components or inside a sealed enclosure. This calculator suggests a rating on that basis, snapping to the standard series of eighth, quarter, half, one, two, three and five watts, with wirewound sizes above that.
Physical size matters as much as the number. A one-watt carbon film resistor is visibly larger than a quarter-watt one because dissipation depends on surface area. If the calculated power is more than a couple of watts, the design question shifts from which resistor to whether a resistor is the right approach at all — a switching regulator wastes far less than a dropper resistor. The resistor colour code calculator and the resistor combination calculator help with identifying and building the values you settle on.
Where DC Ohm's Law Stops Working
Everything on this page assumes direct current through a resistance. Introduce alternating current and two things change. Capacitors and inductors oppose current in a way that depends on frequency and shifts the phase between voltage and current, so the relevant quantity becomes impedance rather than resistance. And voltage times current no longer gives real power, because the two waveforms are no longer in step.
For AC circuits, the equivalent of P = VI picks up a power factor term, and the volt-amperes a supply must deliver exceed the watts the load consumes. Cables and breakers are sized on the former and energy bills on the latter. The power factor calculator covers that relationship, the voltage drop calculator and wire size calculator handle the cable side, and the electricity bill calculator prices the consumption.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using supply voltage for a series component — each part drops only its share, so per-component calculations need the drop across that part alone.
- Forgetting the unit prefix — entering 470 for a 470 kilohm resistor without changing the unit selector overstates the current by a factor of a thousand.
- Applying it to a diode or an LED — non-ohmic devices have no fixed resistance, and dividing their voltage by their current gives a number that is only valid at that one operating point.
- Sizing a resistor at exactly its calculated power — the rating assumes free air at a stated ambient, so a factor of two headroom is the normal working margin.
- Using it on an AC circuit with reactance — capacitors and inductors introduce a phase shift, so impedance replaces resistance and volts times amps no longer gives watts.
Related Free Tools From Arb Digital
Rescale values with the resistance converter. For components, the resistor colour code calculator, the resistor combination calculator and the LED resistor calculator cover identification, combination and current limiting, and the voltage divider calculator covers reference levels. For installations, the voltage drop calculator, the wire size calculator and the electrical power calculator extend the same physics to cables and AC supplies. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
It states that the voltage across a conductor equals the current through it multiplied by its resistance, written V = IR. Rearranged, current equals voltage divided by resistance, and resistance equals voltage divided by current.
Power is voltage times current. Substituting Ohm's law gives two further forms: power equals current squared times resistance, and power equals voltage squared divided by resistance. Which one to use depends on which two quantities you actually know.
Only for purely resistive AC loads. Once capacitance or inductance is involved, the opposition to current becomes impedance, which varies with frequency and shifts the phase between voltage and current, so volts times amps no longer gives real power.
Because it is a non-ohmic device. Below its forward voltage almost no current flows, and above it the current rises steeply for a tiny further increase in voltage, so there is no fixed resistance. That is why an LED needs a series resistor to set its current.
At least twice the calculated dissipation as a working rule, and more if the part sits near other hot components or in a sealed enclosure. The rated wattage assumes free air at a stated ambient temperature, which a crowded board rarely provides.
Yes, in most metals it rises as temperature rises. The extreme case is an incandescent filament, whose cold resistance can be about a tenth of its hot resistance, which is why such lamps draw a large inrush current at switch-on.
The converter rescales a resistance you already have between ohms, kilohms and megohms. This page derives quantities you did not enter — solving for current, resistance or power from the two values you did — using physical relationships rather than unit factors.
This tool is provided for educational and estimating use. It is not a substitute for design work to an applicable wiring or electronics standard, and nothing on this page is electrical installation or safety guidance.
