What are the power formulas?

P = V × I (voltage times current), P = I²R (current squared times resistance), P = V²/R (voltage squared divided by resistance), P = W/t (work divided by time). All three electrical forms are equivalent — choose based on what you know. Units: P in watts, V in volts, I in amps, R in ohms.

How do I convert watts to horsepower?

1 horsepower (mechanical) = 745.7 watts. 1 hp (metric) = 735.5 W. 1 hp (electrical) = 746 W. Divide watts by 745.7 (US) or 735.5 (Europe) to get horsepower. A 1000 W motor = 1.34 hp.

What's the difference between power and energy?

Power (W) is the rate of energy transfer. Energy (J or Wh) is the total amount. A 100 W bulb is power; running it for 10 hours uses 1 kWh of energy. Utility billing uses energy (kWh); appliance ratings use power (W). Power × time = energy.

What is power factor?

Power factor (PF) is the ratio of real power (W) to apparent power (VA) in AC circuits. PF = cos(φ) where φ is the phase angle between V and I. Pure resistive loads: PF = 1. Motors and inductive loads: PF = 0.7-0.85. Low PF means more current drawn for same real power — utilities charge for this on industrial accounts.

How much power does my home use?

Average US household: ~900 kWh/month, or ~1.25 kW continuous. Varies widely by climate, size, and appliances. Big consumers: HVAC (40-60%), water heater (15%), refrigerator (4%), lighting (5-10%), entertainment/computers (5%). Smart meters show real-time use.

How is wind power calculated?

P = ½ × ρ × A × v³ × C_p × η. Where ρ = air density, A = swept area, v = wind speed, C_p = power coefficient (max 0.59 by Betz limit), η = efficiency. Wind power scales with cube of velocity — twice the wind = 8× the power. This is why wind speed matters so much.

What's the maximum power on a 120 V outlet?

Standard 15 A outlet: 120 × 15 = 1,800 W max. NEC recommends only 80% continuous load: 1,440 W. 20 A circuits: 2,400 W max, 1,920 W continuous. 240 V dryer/range circuits: up to 12,000 W. Trying to draw more trips the breaker.

How are solar panels sized in watts?

Panels are rated in watts at Standard Test Conditions (1000 W/m² irradiance, 25°C). A 400 W panel produces 400 W under STC. Real output varies with sun angle, temperature, shading. Typical capacity factor: 18-25%. A 10 kW system produces ~15,000-22,000 kWh/year in average US conditions.

Power Calculator (Watts)

Find electrical power in watts using multiple formulas: P = V × I (voltage times current), P = I²R, P = V²/R, or P = Work/Time. Convert between watts, kilowatts, horsepower, and BTU/hr.

Power is the rate at which energy is transferred, used, or transformed. The SI unit is the watt (W), defined as one joule per second. Every electrical device — light bulb, microwave, refrigerator, EV — is rated in watts (or kilowatts) showing how fast it consumes electrical energy. Mechanical power follows the same definition: a 100 W motor delivers 100 J of work per second.

For electrical circuits, the fundamental power equation is P = V × I (voltage times current). Combining with Ohm's Law (V = IR) gives two useful alternative forms: P = I²R and P = V²/R. All three are equivalent — choose whichever inputs you have. For a device drawing 10 A from a 120 V outlet, P = 120 × 10 = 1,200 W = 1.2 kW. Same device with 12 Ω resistance: P = 100 × 12 = 1,200 W. Or P = 14,400/12 = 1,200 W.

Power equals energy/time, so multiplying power by duration gives total energy: a 100 W bulb running for 10 hours uses 100 × 36,000 = 3,600,000 J = 1 kWh. Utility bills use kWh: a typical US household consumes ~900 kWh/month.

Common applications: electrical engineering (circuit design, motor sizing, transformer ratings), home energy management, vehicle performance (horsepower → watts), industrial process design, renewable energy (solar panel and wind turbine output), and any analysis involving energy delivery rates.

Inputs

Calculate Using

Voltage (V)

Current (A)

Resistance (Ω)

Work/Energy (J)

Time (s)

Results

Power

1,200 W

Kilowatts

1.200 kW

Horsepower

1.609 HP

Power Calculation Results

Parameter	Value
Power	1,200 W
Power (kW)	1.2000 kW
Power (HP)	1.6092 HP
Power (BTU/hr)	4094.57 BTU/hr
Energy per Hour	4,320,000 J
kWh per Day	28.800 kWh
Formula Used	P = V × I

Last updated: May 29, 2026

Formula

**Electrical power formulas:** P = V × I (general) P = I² × R (using current and resistance) P = V² / R (using voltage and resistance) P = W / t (work over time) Where: - P = power (W) - V = voltage (V) - I = current (A) - R = resistance (Ω) - W = work or energy (J) - t = time (s) **Worked example: hair dryer** US hair dryer rated 1,500 W on 120 V mains. I = P/V = 1500/120 = 12.5 A R = V²/P = 14,400/1500 = 9.6 Ω Why circuit breakers trip: a 15 A circuit can't handle this plus another large appliance. **Energy from power × time:** E = P × t (J) E = P × t / 3,600 (kWh, if P in W and t in seconds) E = P × hours × 0.001 (kWh, if P in W and t in hours) A 100 W bulb running 10 hours: 1 kWh. **Power conversions:** | Unit | In watts | |---|---| | 1 W | 1 | | 1 kW | 1,000 | | 1 MW | 10⁶ | | 1 GW | 10⁹ | | 1 TW | 10¹² | | 1 hp (mechanical) | 745.7 | | 1 hp (electrical) | 746 | | 1 hp (metric) | 735.5 | | 1 BTU/hr | 0.293 | | 1 ton refrigeration | 3,517 | | 1 ft·lbf/s | 1.356 | **Common power levels:** | Device/Source | Power | |---|---| | LED bulb (modern) | 7-15 W | | Incandescent bulb | 60-100 W | | Laptop charging | 65-100 W | | Refrigerator (running) | 100-400 W | | Microwave oven | 1,000-1,500 W | | Toaster | 800-1,500 W | | Hair dryer | 1,500-2,000 W | | Window AC | 500-2,500 W | | Central AC | 3,000-5,000 W | | Electric oven | 2,000-5,000 W | | Tesla Plaid motor | 760 kW (1,020 hp) | | Standard rooftop solar | 5-10 kW | | Wind turbine (typical) | 2-3 MW | | Coal plant | 500-1,000 MW | | Nuclear plant (typical) | 1,000-1,500 MW | | Hoover Dam | 2 GW | | Three Gorges Dam | 22.5 GW | | World total | ~3 TW | **Mechanical power:** P = F × v (force times velocity) P = τ × ω (torque times angular velocity) For a 1,500 kg car accelerating at 5 m/s² at 20 m/s: F = 1500 × 5 = 7,500 N P = 7,500 × 20 = 150,000 W = 150 kW = ~200 hp **Power and Ohm's law combined:** | Known | Find P | |---|---| | V, I | P = VI | | V, R | P = V²/R | | I, R | P = I²R | | V, P | I = P/V | | I, P | V = P/I | | R, P | I = √(P/R), V = √(PR) | **Three-phase power:** P = √3 × V_LL × I × cos(φ) Where V_LL = line-to-line voltage, cos(φ) = power factor. For a 480 V (3-phase) motor drawing 50 A at 0.9 PF: P = 1.732 × 480 × 50 × 0.9 = 37,400 W = 37 kW **Real vs reactive vs apparent power (AC):** - **Real power (W)**: actual work done. - **Reactive power (VAR)**: oscillates between source and load. - **Apparent power (VA)**: vector sum. P² + Q² = S² Power factor (PF) = P/S = cos(φ) Industrial loads with motors have PF < 1; power factor correction (capacitors) improves PF, reducing utility billing penalties. **Solar panel sizing:** Power = solar irradiance × area × efficiency At STC (1000 W/m², 25°C): 20%-efficient panel produces 200 W/m². A 5 kW system needs ~25 m² of panels in ideal conditions. **Wind turbine power:** P = ½ × ρ × A × v³ × C_p × η Where: - ρ = air density (1.225 kg/m³) - A = swept area (m²) - v = wind speed (m/s) - C_p ≤ 0.59 (Betz limit) - η = mechanical+electrical efficiency For 10 m diameter rotor at 10 m/s with C_p = 0.4, η = 0.9: P = 0.5 × 1.225 × 78.5 × 1000 × 0.4 × 0.9 ≈ 17.3 kW Wind power scales with v³ — twice the wind = 8× the power. **Mechanical efficiency:** η = P_output / P_input | Device | Typical efficiency | |---|---| | Incandescent bulb | 2-5% | | Fluorescent | 12-25% | | LED | 30-50% | | Internal combustion engine | 25-35% | | Diesel engine | 35-45% | | Electric motor | 85-95% | | Generator | 90-95% | | Solar panel | 18-23% | | Wind turbine | 35-45% | | Hydroelectric | 80-90% | | Thermal power plant | 35-45% | **Energy costs:** US average electricity: ~$0.15/kWh (varies $0.08-$0.45 by region). Annual cost = P (kW) × hours/year × $/kWh A 200 W gaming PC running 8 hours/day, 365 days, at $0.15/kWh: 0.2 × 8 × 365 × 0.15 = $87.60/year

How to use this calculator

Choose calculation method: V×I, I²×R, V²/R, or W/t.
Enter the relevant inputs.
Calculator returns power in watts.
Convert: 1 hp ≈ 746 W; 1 kW = 1.34 hp; 1 BTU/hr ≈ 0.293 W.
For energy: multiply power by time. 1 kWh = 1000 W × 1 hour = 3.6 MJ.
For AC circuits, account for power factor: P = VI × cos(φ).

Worked examples

Microwave oven

**Scenario:** A 1,200 W microwave on 120 V circuit. Current draw? **Calculation:** I = P/V = 1200/120 = 10 A. Add ~10% for transformer losses → actual ~11 A. **Result:** Draws ~11 A — fills most of a 15 A circuit alone. Add another appliance and you may trip the breaker. Modern kitchens often have dedicated 20 A circuits for microwave/disposal/dishwasher.

Tesla Model S motor

**Scenario:** Tesla Model S Plaid motor peaks at 1,020 hp (~760 kW). Energy in 1 hour at full power? **Calculation:** E = 760 × 1 = 760 kWh. **Result:** 760 kWh in one hour — but Tesla battery is only ~100 kWh. So max power can sustain only ~8 minutes. Real driving uses much less (5-20 kW average), giving ~300+ mile range. Peak power for acceleration; cruise power for distance.

Solar panel array

**Scenario:** Home rooftop solar: 25 panels × 400 W = 10 kW peak. Annual energy (US average sunshine)? **Calculation:** Capacity factor ~18% in US average. Annual: 10 kW × 8,760 hr × 0.18 ≈ 15,768 kWh. **Result:** ~15,800 kWh per year. Covers ~80-90% of typical US household consumption (~10,800 kWh/yr). Depending on net metering, could provide $1,500-3,000/year savings at typical electric rates.

When to use this calculator

**Use power calculations for:**

- **Circuit design**: wire sizing, breaker rating, transformer selection. - **Appliance evaluation**: energy cost, circuit capacity. - **Motor sizing**: matching to load. - **Solar/wind sizing**: array capacity vs energy needs. - **Heating/cooling design**: BTU/hr to watts for HVAC. - **Battery sizing**: power × runtime = capacity needed. - **Mechanical engineering**: torque × RPM for motors. - **Industrial process**: pumping, mixing, manufacturing.

**Choosing wire and breakers:**

Standard 120 V US household: - 15 A breaker: 1,800 W max (1,500 W continuous). - 20 A: 2,400 W max (1,920 W continuous). - 30 A: 3,600 W max (dryer outlets).

240 V circuits: - 30 A: 7,200 W (dryers, water heaters). - 50 A: 12,000 W (electric ranges, EV chargers). - 100 A: main panel service common. - 200 A: modern home main service.

**Power factor:**

For AC loads with inductance (motors, transformers, fluorescent lights): - Resistive loads: PF = 1. - Typical motor: PF = 0.7-0.85. - LED drivers: PF = 0.5-0.99 (varies).

Utility companies charge industrial users for low PF since reactive power increases distribution losses. Power factor correction capacitors raise PF to 0.95+, reducing bills.

**Energy storage (battery sizing):**

For a backup that powers 1 kW for 10 hours: - Energy needed: 10 kWh. - Allow 20% derating: 12 kWh nominal. - Tesla Powerwall: 13.5 kWh = good match.

**Heating efficiency:**

Heat pumps: COP (coefficient of performance) > 1. - Air-source: COP 2-4 (300% efficient). - Geothermal: COP 3-5 (400% efficient).

Resistance heating: COP = 1. Gas furnaces: 80-98% efficient.

This is why heat pumps are typically 2-4× more efficient than electric resistance heating for the same heat output.

**Common applications:**

- **Home energy audits**: identifying high-power devices. - **Electrical safety**: ensuring circuits aren't overloaded. - **EV charging**: Level 1 (~1.4 kW), Level 2 (3-19 kW), DC Fast (50-350 kW). - **Server farms**: cooling = ~40% of total power. - **Cryptocurrency**: Bitcoin network ~150 TWh/yr globally (comparable to Argentina). - **Industrial motors**: 65% of industrial electricity globally.

**Software:**

- **Watt meters** (Kill-A-Watt, smart plugs): measure real consumption. - **Energy monitors** (Sense, Emporia): whole-house monitoring. - **PowerWorld**: utility-scale power flow analysis. - **Spreadsheets**: simple budgeting and sizing.

**Pitfalls:**

- **Confusing power and energy**: P (W) is rate; E (Wh, J) is total. - **Mixing real and apparent power**: VA vs W (matters for AC). - **Ignoring power factor**: undersize equipment for inductive loads. - **Using nameplate ratings as actual**: real consumption varies. - **Forgetting standby power**: many devices consume even when "off". - **Mixing units**: HP vs kW vs BTU/hr vs ton. - **Adding watts when shouldn't (or vice versa)**: parallel adds; series doesn't (for resistors).

Common mistakes to avoid

Confusing power (W) with energy (Wh or J).
Mixing AC real, reactive, and apparent power.
Forgetting power factor in AC calculations.
Treating peak power as continuous (most devices can't sustain).
Using DC formulas for AC without accounting for RMS values.
Mixing units (kW vs HP vs BTU/hr).
Ignoring efficiency when comparing energy systems.
Forgetting standby/idle power consumption.

Frequently Asked Questions

Sources & further reading

SponsoredShop Top Deals on AmazonSupport CalcMountain — browse top-rated products at no extra cost to you.