⚡ Electrical Power and Energy: The Complete DIY Guide (Formulas, Real Examples & Battery Math)
Hey makers! Electro here. Why does your ESP32 battery die in one day? Why does a 100 W resistor get smoking hot while a 100 W LED bulb stays cool? Why does your electricity bill jump in winter? The answer to all of these is the same two concepts: electrical power and electrical energy. Today we're turning the boring textbook formulas into practical tools you'll use in every single DIY project — from sizing a power supply to estimating battery runtime and reading your electricity bill like an engineer.
🔄 Updated for 2026: real maker examples (ESP32, LED strips, amplifiers), battery Wh math, electricity bill calculations, and how to measure real consumption with an INA219 or an ESP32 energy monitor.
🔌 Electrical Power: The Three Formulas
When a direct current of I amperes is flowing in an electric circuit and the voltage across the circuit is V volts, then the power, in watts, is:
P = V × I
Combine it with Ohm's law (V = I×R) and you get the other two forms — three formulas, one physics. Pick whichever matches the two values you have on hand:
| Formula | Derived by substituting | Use it when you know... |
|---|---|---|
| P = V × I | Definition of power | Voltage and current |
| P = I² × R | V = I×R | Current and resistance (cable & resistor heating!) |
| P = V² / R | I = V/R | Voltage and resistance (fixed-voltage rails) |
🧮 Real Maker Examples
| Device | Voltage | Current | Power |
|---|---|---|---|
| ESP32 (WiFi on) | 3.3 V | 240 mA | ≈ 0.8 W |
| LED strip (1 m, 5050) | 12 V | 1.2 A | 14.4 W |
| Resistor 100 Ω @ 100 mA | 10 V | 0.1 A | P = I²R = 1 W → use a 2 W part! |
| Car amplifier | 12 V | 15 A | 180 W |
| Kettle | 230 V | 8.7 A | ≈ 2000 W |
🔋 Electrical Energy: Power × Time
Electrical energy = power × time (E = P × t). With power in watts and time in seconds, the unit of energy is the watt-second or joule: E = V×I×t joules. Power tells you how fast; energy tells you how much in total.
Although the unit of energy is the joule, when dealing with large amounts of energy the unit used is the kilowatt-hour (kWh) — the famous "unit of electricity" your home meter counts:
- 1 kWh = 1000 watt-hours
- 1 kWh = 1000 × 3600 watt-seconds = 3,600,000 J (3.6 MJ)
Bill example: a 2000 W heater running 3 h consumes 2 × 3 = 6 kWh. At €0.22/kWh, that's €1.32 per session. Now you can read your bill like an engineer!
🤖 The Maker Twist: Battery Capacity is Energy Too
Here's the formula every DIYer must know — battery capacity in watt-hours:
Wh = V × Ah
Example: a 12 V / 105 Ah battery stores 12 × 105 = 1260 Wh. Running a 60 W load: 1260 / 60 = 21 h theoretical — but lead-acid should never discharge below 50%, so plan for ≈ 10 h. This single calculation is the foundation of my camping-car solar guide and every UPS project on this blog.
And it explains why deep sleep matters: an ESP32 drops from 240 mA to ~10 µA in deep sleep — the same formula shows why your battery lasts months instead of days.
📏 Measure, Don't Guess (Pro Method)
- INA219 module: an I2C sensor that reads voltage, current and power directly — perfect with Arduino/ESP32.
- Multimeter in series: quick and dirty current check on the 10 A range.
- Then build my ESP32 Smart Energy Monitor to log kWh in real time.
💡 Pro Tips (by Electro)
- Power supply headroom: size your PSU at 1.3× the calculated load (a 60 W project → 80-100 W PSU).
- Resistor rating: always double the calculated dissipation (1 W calculated → 2 W part). Heat is the #1 killer of DIY boards.
- P = I²R explains wiring fires: double the current = 4× the heat in cables. That's why a 15 A load needs thick wire, not speaker wire!
- AC vs DC: P = V×I is exact for DC and resistive AC loads (heaters, incandescent). For motors and PSU loads, add the power factor: P = V×I×PF.
❓ FAQ
What's the difference between power and energy?
Power is the rate (watts) — like speed. Energy is the total (watt-hours or joules) — like distance. A 100 W bulb left on for 10 h uses 1 kWh.
Why three power formulae instead of one?
They're the same law rearranged with Ohm's law. Use P = I²R when current is known (cable heating), P = V²/R when voltage is fixed (choosing a resistor), and P = V×I for everything else.
How long will a 12 V battery run my fridge?
Wh = V×Ah, then divide by the average load. A 100 Ah battery (≈1200 Wh, 50% usable = 600 Wh) running a fridge averaging 50 W gives ≈ 12 h. See my camping-car solar guide for the full method.
🎯 Conclusion
Power and energy are not textbook abstractions — they're the two numbers behind every design decision you'll ever make: PSU sizing, battery runtime, cable thickness, resistor ratings, and your electricity bill. Master P = V×I and E = P×t, and you've just upgraded from copying circuits to truly engineering them.
What's the most surprising consumption you've ever measured on a project? Share it in the comments — I read every one!
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