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📐 Ohm's Law & Power Formula Wheel (All 12 Equations)
A complete formula wheel for the relationships between P (Power), V (Voltage), I (Current), and R (Resistance). To use it, pick the variable you want to solve for in the inner circle, then read the formula in the outer ring for the two values you know.
Power (P)
24.00 W
Voltage (V)
12.00 V
Current (I)
2.00 A
Resistance (R)
6.00 Ω
📘 All 12 Power Formulas
P = I² × R
P = V² / R
V = I × R
V = √(P × R)
I = V / R
I = √(P / R)
R = V² / P
R = P / I²
📊 Step-by-Step Calculation
DC Power Calculator: The Complete Guide to Watts, Volts, Amps & Ohms
This DC power calculator instantly computes the unknown value among Power (watts), Voltage (volts), Current (amps), and Resistance (ohms) when you supply any two of the others. It implements the full 12-formula Ohm's Law power wheel built from two fundamental laws — Ohm's Law (V = I × R) and the power law (P = V × I) — and shows the working step by step. Use it for circuit design, component sizing, troubleshooting, electronics homework, and quick sanity checks at the bench.
Quick Answer: The Three Main DC Power Formulas
| If you know… | …use this formula | Example (12V, 2A, 6Ω) |
|---|---|---|
| Voltage & Current | P = V × I | P = 12 × 2 = 24 W |
| Current & Resistance | P = I² × R | P = 2² × 6 = 24 W |
| Voltage & Resistance | P = V² / R | P = 12² / 6 = 24 W |
What Is DC Electrical Power?
DC (direct current) power is the rate at which electrical energy is converted into another form of energy — heat, light, motion, or sound — inside a DC circuit. It is measured in watts (W), named after James Watt. One watt equals one joule of energy transferred per second, or equivalently, one volt multiplied by one ampere. Unlike AC power, DC power has no phase angle or reactive component, so the calculation is purely the product of voltage and current at any instant.
The Three Core DC Power Formulas Explained
2. P = I² × R — Substituting V = IR into P = VI. Used when current and resistance are known.
3. P = V² / R — Substituting I = V/R into P = VI. Used when voltage and resistance are known.
All three formulas are algebraically equivalent through Ohm's Law (V = IR).
The Complete 12-Formula Power Wheel
Combining Ohm's Law with the power law produces twelve formulas that relate any two of the four quantities — P, V, I, R — to the other two. This is the Ohm's Law power wheel shown in the calculator above:
Find Voltage (V): V = P/I | V = I×R | V = √(P×R)
Find Current (A): I = P/V | I = V/R | I = √(P/R)
Find Resistance (Ω): R = V/I | R = V²/P | R = P/I²
To use the wheel, choose the variable you want to solve for in the inner circle, then read the formula in the outer ring that contains the two variables you already know.
Understanding Each Variable
- Power (P) — watts (W): The rate of energy transfer. A 60 W lamp converts 60 joules of electrical energy per second into light and heat.
- Voltage (V) — volts (V): The electrical "pressure" that pushes current through a circuit. Higher voltage means more force driving the electrons.
- Current (I) — amperes (A): The flow rate of electric charge. One ampere equals one coulomb of charge passing a point per second.
- Resistance (R) — ohms (Ω): Opposition to current flow. Higher resistance means less current for a given voltage.
Worked Examples
Example 1: Power from Voltage and Current (P = VI)
Problem: A 12 V battery drives 2 A through a circuit. What is the power?
Solution: P = V × I = 12 × 2 = 24 W
Example 2: Power from Voltage and Resistance (P = V²/R)
Problem: 120 V is applied across a 240 Ω heating element.
Solution: P = V² / R = 14,400 / 240 = 60 W
Example 3: Power from Current and Resistance (P = I²R)
Problem: 0.5 A flows through a 100 Ω resistor.
Solution: P = I² × R = 0.25 × 100 = 25 W
Example 4: Current from Power and Voltage (I = P/V)
Problem: A 100 W device on a 12 V supply. How much current does it draw?
Solution: I = P / V = 100 / 12 = 8.33 A
When to Use Each Formula
| Scenario | Best Formula | Why |
|---|---|---|
| Sizing a power supply for a load | P = V × I | You usually know supply voltage and load current |
| Calculating heat in a resistor | P = I² × R | Resistor value and current through it are usually known |
| Heater element on fixed voltage | P = V² / R | Mains/supply voltage and element resistance are fixed |
| Battery runtime estimate | I = P / V | Use battery voltage and device wattage |
| Choosing a current-limiting resistor | R = V / I | Voltage across the resistor and desired current are known |
Practical Applications of DC Power Calculations
- Wire and trace sizing: Power determines heat dissipation. Higher power needs thicker conductors to prevent overheating and meet ampacity limits.
- Battery life and capacity: Battery energy (Wh) divided by load power (W) gives runtime in hours. Use this for portable electronics and solar systems.
- Component selection: Resistors, MOSFETs, BJTs, voltage regulators, and diodes must each be rated above the power they will dissipate, with safety margin.
- Solar panel and off-grid sizing: Total load power and daily run-hours determine panel wattage, battery bank size, and charge controller current.
- Fuse and breaker selection: Calculate the worst-case current (I = P/V) and choose a fuse rated above it but below the wiring's safe limit.
- Energy cost estimation: Power (kW) × time (hours) = energy (kWh). Multiply by your electricity rate for cost. Useful for evaluating efficient appliances.
- LED driver design: Knowing forward voltage and target current lets you size the series resistor (V/I) and verify its power rating (I²R).
- Heat sinking: Calculated power dissipation determines the required thermal resistance of the heat sink.
Common DC Voltages and Typical Power Levels
| DC Voltage | Common Use | Typical Power |
|---|---|---|
| 1.5 V | Alkaline AA / AAA cell | 0.5 – 2 W |
| 3.3 V | MCU / SoC rail | 0.1 – 5 W |
| 3.7 V | Lithium-ion cell (nominal) | 3 – 50 W |
| 5 V | USB / logic supply | 2.5 – 100 W (USB-PD) |
| 12 V | Automotive / LED strips | 10 – 240 W |
| 24 V | Industrial control, solar | 50 – 1000 W |
| 48 V | Telecom, e-bikes, datacenters | 100 – 5000 W |
Quick Conversions: Watts ↔ Amps ↔ Volts
- Watts to amps: Amps = Watts ÷ Volts (e.g., 60 W ÷ 12 V = 5 A)
- Amps to watts: Watts = Volts × Amps (e.g., 12 V × 5 A = 60 W)
- Watts to volts: Volts = Watts ÷ Amps (e.g., 60 W ÷ 5 A = 12 V)
- Volts to watts (with R): Watts = Volts² ÷ Ohms (e.g., 12² ÷ 2.4 = 60 W)
Power Unit Reference
- 1 kW = 1,000 W
- 1 MW = 1,000,000 W
- 1 mW = 0.001 W
- 1 hp (horsepower) ≈ 746 W
- 1 BTU/hour ≈ 0.293 W
- 1 kWh = 3,600,000 joules
DC Power vs. AC Power
In a DC circuit the voltage and current are constant, so power is simply P = V × I and is always positive (energy flows from source to load). In an AC circuit the voltage and current vary sinusoidally, and when the load contains inductance or capacitance, current and voltage are no longer in phase. AC analysis then introduces three different "powers": real power (P, in watts), reactive power (Q, in VAR), and apparent power (S, in VA), related by the power factor cos(φ). This calculator focuses on DC; for AC analysis use a separate AC power calculator.
Frequently Asked Questions
What are the three DC power formulas?
P = V × I, P = I² × R, and P = V² / R. All three give the same answer for any given DC circuit; choose the one that matches the values you already know.
How do I calculate watts from volts and amps?
Multiply them. Watts = Volts × Amps. A 12 V supply delivering 2 A is producing 24 watts.
How many watts is 12V 2A?
24 watts (12 × 2 = 24). The same applies for any voltage × current pair in DC.
How do I calculate amps from watts and volts?
Divide: Amps = Watts ÷ Volts. A 60 W load on a 12 V supply draws 60 / 12 = 5 A.
What is the difference between power and energy?
Power is the rate at which energy is transferred (watts = joules per second). Energy is the total amount transferred over time (joules or watt-hours). A 100 W bulb running for 10 hours consumes 1,000 Wh = 1 kWh of energy.
Does P = VI work for AC circuits?
Only for purely resistive AC loads, and only when V and I are RMS values. For loads with reactance, real power requires the power factor: P = V × I × cos(φ).
Why does doubling the voltage quadruple the power?
Because P = V² / R. Doubling V (at constant R) doubles the current as well, so power increases by 2 × 2 = 4×. This is why high-voltage transmission lines minimize I²R losses.
What is the power triangle / power wheel?
The power wheel is a circular diagram that lays out all 12 formulas relating P, V, I, and R. Pick the variable you want in the center; the outer ring shows the formula to use depending on which two variables you know.
Why does a resistor get hot?
Because of the I²R power it dissipates. Every watt of dissipated power becomes heat. This is also called joule heating.
Related Electrical Calculators
- Ohm's Law Calculator — V = IR with interactive circuit visualization
- AC Power Calculator — real, reactive, and apparent power
- Series Resistor Calculator
- Parallel Resistor Calculator
- Resistor Wattage Calculator — pick the right power rating
- LED Resistor Calculator
- Battery Capacity Calculator — mAh / Wh / runtime