What Ohm's law actually says
Ohm's law is the one equation everyone who has ever picked up a soldering iron remembers. Georg Ohm published it in 1827 after a decade of patient experiments with copper wire, and the relationship has not budged since. In its most familiar form:
V = I × R
Voltage equals current times resistance.
Voltage is the electrical pressure pushing electrons along. Current is how many electrons per second flow past a given point. Resistance is the wire or component pushing back against that flow. The three quantities live in lockstep: change any one and the others must move to balance the equation.
The Ohm's Law Calculator handles all four variables at once — voltage, current, resistance, and power — and you pick any two of them. The other two fall out automatically. No re-arranging the formula in your head, no scratching out exponents on a napkin.
Four variables, one equation, six rearrangements
Once you bring power into the picture, the family grows. Power equals voltage times current:
P = V × I
Substitute Ohm's law in and you get two more useful forms:
P = I² × R (power equals current squared times resistance)
P = V² ÷ R (power equals voltage squared divided by resistance)
That is six equations covering every pair of inputs you might have. The calculator picks the right one for you. The thing to notice is the squaring. Double the current and the heat in the wire goes up by a factor of four. This is why high-current circuits demand thicker wires, why fuses blow on small overloads, and why your laptop charger gets warm but does not melt.
Worked example: a 12-volt LED strip
Here is a problem you might actually run into. You are wiring an LED strip to a 12-volt power supply. The strip draws 500 milliamps. What is its resistance, and how much power is it pulling from the supply?
You know two of the four variables: V = 12 V, I = 0.5 A. The calculator solves the rest:
- Resistance: R = V ÷ I = 12 ÷ 0.5 = 24 Ω
- Power: P = V × I = 12 × 0.5 = 6 W
Six watts is well within the comfort zone of a typical 12-volt 1-amp wall wart, which can deliver up to 12 watts. Good — the strip will run cool and the supply will not strain.
Now flip the problem. You want to use a 9-volt battery instead. What current will the same 24-ohm strip pull, and how much power?
- I = V ÷ R = 9 ÷ 24 = 0.375 A (375 mA)
- P = V × I = 9 × 0.375 = 3.375 W
Less voltage means less current and far less power — 56% of what the strip drew on 12 volts. The strip will glow noticeably dimmer. A 9V alkaline battery rated 500 mAh would run the strip for about 1.3 hours before going dead.
Engineering prefixes — milli, kilo, mega, micro
Real-world electrical numbers span thirty orders of magnitude. A scientist measuring radio waves works with nanoamps; an electric utility moves megawatts. Writing all those zeros gets old fast, so engineers use SI prefixes:
| Prefix | Symbol | Multiplier | Common example |
|---|---|---|---|
| giga | G | ×1,000,000,000 | 1 GHz CPU clock |
| mega | M | ×1,000,000 | 1 MΩ multimeter input |
| kilo | k | ×1,000 | 4.7 kΩ pull-up resistor |
| (none) | — | ×1 | 1 A wall outlet draw |
| milli | m | ÷1,000 | 20 mA LED current |
| micro | µ | ÷1,000,000 | 10 µA op-amp input bias |
| nano | n | ÷1,000,000,000 | 5 nA leakage current |
The Ohm's Law Calculator picks the prefix automatically. Enter 0.004 amps and it shows 4 mA. Enter 4,700 ohms and it shows 4.7 kΩ. You stop counting zeros and start thinking about the circuit.
Picking an LED current-limiting resistor
This is the canonical Ohm's law homework problem and one of the most common real uses of the calculator. Say you have a red LED that wants 2 V across it at 20 mA forward current, and you want to power it from a 5-volt logic supply. What resistor do you put in series with the LED?
The resistor has to drop the difference: 5 V minus 2 V equals 3 V. The same current that flows through the LED flows through the resistor (it is a series circuit), so the resistor sees 20 mA. Plug those into the calculator:
- R = V ÷ I = 3 ÷ 0.020 = 150 Ω
- P = V × I = 3 × 0.020 = 0.06 W
You would pick the nearest standard value — 150 Ω is itself a standard E12 resistor, so done. The 0.06 W power dissipation is well under a quarter-watt resistor's rating, so almost any through-hole resistor will work. If you only have 220 Ω in the parts drawer, that works too — the LED will run at about 13.6 mA instead of 20, slightly dimmer but completely safe.
How much current does your stuff actually pull?
The numbers people quote get fuzzy fast. Here is what common household devices actually draw from a US 120-volt outlet, computed straight from each device's wattage with I = P ÷ V.
| Device | Wattage | Current at 120 V |
|---|---|---|
| 9-watt LED bulb | 9 W | 0.075 A (75 mA) |
| Laptop charger (60W) | 60 W | 0.50 A |
| WiFi router | 12 W | 0.10 A |
| Desktop PC + monitor | 300 W | 2.5 A |
| Refrigerator (running) | 180 W | 1.5 A |
| Microwave oven | 1,440 W | 12.0 A |
| Toaster | 1,200 W | 10.0 A |
| Hair dryer (high) | 1,500 W | 12.5 A |
| Electric space heater | 1,500 W | 12.5 A |
| Window AC unit (10,000 BTU) | 1,000 W | 8.3 A |
The reason a typical US wall outlet is on a 15-amp breaker is that anything beyond about 12 amps continuous risks tripping it. Run a microwave and a hair dryer on the same circuit and you have already overshot. This is also why electric kettles in 120-volt countries are slower than their 240-volt cousins — at 1,500 watts the kettle is already near the outlet limit, so it cannot boil as fast as a UK kettle pulling 3,000 watts at 240 V.
Does Ohm's law work for AC?
Yes — with one footnote. The same V = I × R holds for the magnitudes of AC voltage and current, as long as you use RMS values. RMS (root-mean-square) is the AC equivalent of DC value: a 120-volt RMS sine wave delivers the same average power to a resistor as a steady 120-volt DC source.
For purely resistive loads — incandescent bulbs, electric heaters, toasters — Ohm's law and P = V × I are exact. The calculator gives the right answer.
For reactive loads — motors, transformers, fluorescent ballasts — voltage and current go out of phase. The real average power becomes P = V × I × cos(φ), where φ is the phase angle and cos(φ) is the "power factor." A typical induction motor has a power factor around 0.85, which means apparent power (in volt-amps) is larger than real power (in watts). The Ohm's Law Calculator assumes power factor = 1, which is correct for resistive loads and a reasonable approximation for most consumer electronics.
Why current squared shows up in P = I²R
The squaring is one of the most useful consequences of the equation. Substitute V = I × R into P = V × I and you get P = I × R × I = I² × R. Mathematically equivalent. Physically important.
It means heat dissipation scales with the square of current. Double the current and the wire gets four times hotter. Triple it and the wire gets nine times hotter. This is why:
- High-voltage transmission lines use the highest practical voltage. The same power at higher voltage means less current, and less current means dramatically less I²R loss in the wire.
- Fuses do not blow at exactly their rated current — they blow on the heat from sustained or surge currents. A 10-amp fuse handles 9 amps indefinitely but pops on a 30-amp inrush within milliseconds because the heating goes as 30² = 900 versus 9² = 81.
- USB-C fast charging at 20 V is enormously more efficient than at 5 V for the same wattage. At 5 V × 18 W you need 3.6 A; at 20 V × 18 W you need 0.9 A. The cable losses drop to about 6% of what they were.
Related calculations
Ohm's law is the foundation. The follow-on tools handle specific applications:
- Voltage Drop Calculator — for wire runs longer than a few feet. Calculates how much voltage you lose between source and load based on AWG gauge, length, and current. The numbers come straight from Ohm's law applied to the wire's resistance.
- Horsepower Calculator — when the electrical math meets motor math. One horsepower equals 745.7 watts, so an electric motor's HP rating times 745.7 gives you input watts (before accounting for efficiency).
- BTU Calculator — for sizing heaters and air conditioners. Watts and BTU/hr are both rates of energy transfer; 1 watt = 3.412 BTU/hr.
- Temperature Converter — pairs with I²R heating calculations when you are computing how hot a resistor or wire will get.
Frequently asked questions
Why does my multimeter read slightly different from the calculator?
Real components have tolerances. A "10 kΩ" resistor marked with a gold band has ±5% tolerance — it might actually be anywhere from 9,500 Ω to 10,500 Ω. Brown-band 1% resistors are tighter but still not exact. Wall outlet voltage is also not perfectly 120 V; the US grid runs anywhere from about 114 to 126 V depending on time of day and distance from the substation. The calculator gives the ideal answer; the multimeter shows you the messy real one.
Does Ohm's law apply to diodes and transistors?
Not directly. Ohm's law assumes a linear relationship between voltage and current — double the voltage, double the current. Diodes and transistors are nonlinear: a silicon diode passes almost no current until you reach about 0.6 V, then conducts heavily. For these, you use the device's I-V curve from the datasheet, not Ohm's law. The calculator is for resistive components.
What is the highest resistance the calculator can handle?
It works in double-precision floating point, so up to about 1.8 × 10^308 in any variable and down to about 5 × 10^-324. Real electrical applications never approach those limits. A 1 TΩ (terohm) insulator and a 1 pA (picoamp) leakage current are both well within range.
If I know the resistance, can I just plug in different voltages to see what happens?
Yes — that is exactly the workflow the calculator was designed for. Lock in R, sweep V, and watch I and P track. This is the standard sanity check before powering up any new circuit: at the worst-case input voltage, is the current still safe? Is the power dissipation under the resistor's rating? If yes, the circuit is good.
What is the difference between watts and watt-hours?
Watts is a rate — how fast you are using energy right now. Watt-hours is a quantity — how much energy you used over a period of time. A 100-watt bulb left on for 10 hours uses 1,000 watt-hours, or 1 kilowatt-hour. Your power company bills you in kilowatt-hours. The Ohm's Law Calculator handles watts; to get watt-hours, multiply by the number of hours.
Why is my calculation off by a factor of 1,000?
Almost always a unit error. The most common one: entering 20 (meaning milliamps) when the calculator expects amps. 20 amps and 20 milliamps are 1,000× different. The Ohm's Law Calculator's auto-prefix display helps catch this — if you see "20 A" in the output and you meant 20 mA, you know to re-enter as 0.020 or use the mA unit toggle.
Can I use the calculator for battery sizing?
Yes, with one extra step. Calculate the current draw from the load using Ohm's law, then divide the battery's amp-hour rating by that current to get runtime in hours. A 2,500 mAh AA battery running a 50 mA circuit lasts 2,500 ÷ 50 = 50 hours in theory. Real batteries lose capacity at higher currents and lower temperatures, so plan for about 70–80% of the rated runtime.