The 12 formulas behind every calculation here
Power, voltage, current, and resistance are locked together by two short equations — Ohm's law (V = I × R) and Watt's law (P = V × I) — and combining them gives every quantity three different ways to solve for it, depending on which two values you have on hand:
| To find | From V & I | From V & R | From I & R |
|---|---|---|---|
| Power (P) | P = V × I | P = V² ÷ R | P = I² × R |
| Voltage (V) | from P & I: V = P ÷ I | V = I × R | from P & R: V = √(P×R) |
| Current (I) | from P & V: I = P ÷ V | I = V ÷ R | from P & R: I = √(P÷R) |
| Resistance (R) | R = V ÷ I | from V & P: R = V² ÷ P | from P & I: R = P ÷ I² |
You don't need to memorise all 12 — just pick the calculation type and the two values you already know, and the calculator applies the matching formula automatically. If you only ever need the plain V = I × R relationship, the Ohm's Law Calculator is a more focused version of that single formula.
From volts to dollars: a full worked example
Here's how the chain from raw electrical values to a dollar figure on a bill actually runs, start to finish:
- Start with 120 V across a 24 Ω heating element. Power = V² ÷ R = 120² ÷ 24 = 600 W.
- Run it for 5 hours: Energy = 600 W × 5 h = 3,000 Wh = 3 kWh.
- At a rate of $0.15 per kWh: Cost = 3 kWh × $0.15 = $0.45 for that one 5-hour run.
That's the same three-step chain — electrical values → power → energy over time → cost — behind every device on a utility bill, just usually run in reverse: the label tells you the wattage, you estimate the hours, and the calculator gives you the dollar figure.
Estimating your electric bill from appliance usage
Most appliances list their wattage on a nameplate, sticker, or in the manual. If you only have volts and amps instead, multiplying them gives a reasonable estimate of watts for simple resistive loads like heaters and incandescent bulbs — though motors and electronics with power factors below 1 will draw somewhat more apparent power than that simple multiplication suggests.
| Appliance | Typical power |
|---|---|
| LED light bulb | ~10 W |
| Laptop | ~50 W |
| Refrigerator (running) | ~150 W |
| Microwave | ~1,000 W |
| Window AC unit | ~1,000 W |
| Space heater / hair dryer | ~1,500 W |
These are rough, commonly cited averages — check the actual nameplate for anything you're budgeting seriously around, since efficiency varies a lot between models.
Power unit conversions
| Unit | Equals |
|---|---|
| 1 horsepower (hp) | 745.7 W |
| 1 BTU/h | 0.293 W |
| 1 W | ~3.412 BTU/h |
Horsepower shows up when comparing electric motors to engines; BTU/h is the unit heating and cooling equipment is rated in — the BTU Calculator covers that side in more depth. If you're working with resistors specifically, or need to check voltage loss over a long run of wire, see the Resistor Calculator and Voltage Drop Calculator.