Acceleration Calculator
Calculate acceleration from velocity change and time, force and mass, or centripetal motion. Convert between m/s², g-force, ft/s², and more.
Work and Power Calculator
Calculate mechanical power using P = W/t and P = Fv. Supports efficiency modeling, unit conversions (watts, hp, BTU/hr), and real-world power comparisons.
Common Scenarios
Mechanical efficiency
%
N
m
s
Power Output⧉
1.00 kW
1.34 hp
Work / Energy⧉
5.00 kJ
1.195 kcal • 0.001389 kWh
Force⧉
500.00 N
50.99 kgf
Velocity⧉
2.00 m/s
7.2 km/h
Power (BTU/hr)⧉
3,412.00 BTU/hr
Heating/cooling equivalent
Power (ft·lbf/s)⧉
737.60 ft·lbf/s
Imperial power unit
Power Comparison Reference
| Reference | Power (W) | Your Result Comparison |
|---|---|---|
| LED light bulb | 10 W | 100.0× |
| Human sustained | 75 W | 13.3× |
| Horse sustained | 746 W | 1.3× |
| Microwave oven | 1 kW | 1.0× |
| Small car engine | 75 kW | 1.3% |
| Locomotive | 3,000 kW | 0.0% |
| Wind turbine | 2,500 kW | 0.0% |
Planning notes, formulas, and examples
About the Work and Power Calculator
The work and power calculator computes mechanical power — the rate at which work is done or energy is transferred — using the fundamental relationships P = W/t and P = Fv. While work measures total energy transferred, power tells you how fast that transfer happens, making it the critical specification for motors, engines, turbines, and any device that converts energy.
Power determines whether a task is practically feasible. A human can produce about 75 watts sustained (roughly 0.1 hp), enough to climb stairs slowly but not to power a car. A car engine producing 150 kW (201 hp) can accelerate a 1500 kg vehicle because it delivers energy fast enough to overcome drag and inertia at highway speeds.
This calculator offers four computation modes: power from work and time (P = W/t), power from force and velocity (P = Fv), energy from power and duration (W = Pt), and kinetic energy to power conversion. It includes efficiency modeling to account for real-world losses, multi-unit output (watts, horsepower, BTU/hr, ft·lbf/s), and a comparison table showing your result against common power references from LED bulbs to locomotives.
When This Page Helps
Power is the universal specification for machines and energy systems. Every motor, engine, generator, and appliance is rated by power — it tells you what the device can do per unit time. This calculator connects the physics definition (P = W/t = Fv) to practical engineering through efficiency modeling, multi-unit conversion, and real-world comparisons.
The efficiency feature is particularly valuable for real engineering problems. A pump rated at 5 kW output with 80% efficiency actually draws 6.25 kW from the electrical supply and dumps 1.25 kW as heat. Without accounting for efficiency, motors are undersized and electrical systems overloaded.
How to Use the Inputs
- Select the calculation mode: P = Fd/t, P = Fv, W = Pt, or kinetic energy mode
- Enter the known quantities — force, distance, time, velocity, mass, or power depending on mode
- Set the efficiency percentage to account for mechanical losses (100% = ideal)
- Use preset buttons for common scenarios like a sprinter, car engine, or elevator
- Read power output in watts, kW, horsepower, and BTU/hr from the output cards
- If efficiency < 100%, check the input power required and power lost to heat
- Compare your result against reference power levels in the comparison table
Formula used
Power from work: P = W/t = Fd/t
Power from force and velocity: P = Fv = F · d/t
With efficiency: P_output = η × P_input
Where:
• P = power (W = J/s)
• W = work (J = N·m)
• t = time (s)
• F = force (N)
• v = velocity (m/s)
• η = efficiency (0 to 1)
Unit conversions:
• 1 hp = 745.7 W
• 1 kW = 1.341 hp
• 1 W = 3.412 BTU/hr
• 1 W = 0.7376 ft·lbf/sExample Calculation
Result: Power = 1000 W (1.34 hp)
A 500 N force applied over 10 m in 5 seconds: W = Fd = 5000 J, P = W/t = 5000/5 = 1000 W = 1.34 hp. This is about 13 times the sustained power output of an average human (75 W), roughly equivalent to a small portable generator.
Tips & Best Practices
- For electric motors, typical efficiency is 85-95% — always account for this when sizing the electrical supply
- Quick hp estimate: 1 hp ≈ 750 W, so divide watts by 750 for approximate horsepower
- At constant speed, all engine power goes to overcoming resistance (drag + rolling friction + grade)
- Power to climb: P = mgv_vertical — a 70 kg person climbing stairs at 0.5 m/s vertical needs 343 W
- Energy cost: multiply kW by hours and $/kWh to get operating cost — 1 kW for 1 hour at $0.12/kWh = $0.12
- Peak vs sustained power differ greatly — a car engine peaks at 150 kW but cruises at 20-30 kW
Power in Engineering Design
Power ratings are the primary specification for machines because they tell engineers what the machine can accomplish per unit time. A 10 kW motor can lift a 1000 kg load at 1 m/s, or a 500 kg load at 2 m/s, or a 100 kg load at 10 m/s — the power sets the product of force and speed, and the engineer chooses the gearing to match the application.
This is why transmissions exist in vehicles. An engine produces power P = τω (torque × angular velocity) that's roughly constant across a range of RPM. A transmission trades torque for speed: low gear gives high force (torque) at low speed for hill climbing, while high gear gives low force at high speed for cruising. The total power is the same in both cases.
Efficiency and Energy Losses
No real machine converts energy at 100% efficiency. Electric motors lose energy to resistance heating in windings (I²R losses), magnetic hysteresis in the core, friction in bearings, and air resistance. A typical induction motor is 85-95% efficient. Combustion engines fare much worse: a gasoline engine is 25-35% efficient, with most energy lost as waste heat and exhaust.
System efficiency is the product of individual component efficiencies. A pump system with a 90% efficient motor, 85% efficient pump, and 95% efficient variable-frequency drive has overall efficiency of 0.90 × 0.85 × 0.95 = 72.7%. To deliver 10 kW of hydraulic power, the electrical input must be 10/0.727 = 13.8 kW, with 3.8 kW wasted as heat.
Power Scaling Laws
Many physical systems have power requirements that scale non-linearly with speed. Aerodynamic drag force scales as v², so the power to overcome drag scales as Fv = v² × v = v³. Doubling a car's speed from 60 to 120 km/h requires 8× the power to overcome air resistance — this is why fuel economy drops dramatically at highway speeds.
Similarly, pumping power for fluids scales roughly as the cube of flow rate (since pressure drop scales as flow² and power = pressure × flow). A fan running at 80% speed uses only (0.8)³ = 51% of the power at full speed — the basis for enormous energy savings from variable-speed drives in HVAC systems.
Sources & Methodology
Last updated:
Frequently Asked Questions
Work (joules) measures the total energy transferred: W = Fd. Power (watts) measures the rate of transfer: P = W/t. Two cranes lifting the same 1-ton load 10 m do the same work (98,100 J), but the one that does it in 10 seconds uses 10× more power (9,810 W vs 981 W for 100 seconds) than the other.
P = W/t = Fd/t = F(d/t) = Fv. This form is especially useful for steady-state problems where force and speed are constant, like a car cruising at highway speed. The engine power equals the total drag force times the velocity. It's also why top-speed power requirements scale with the cube of velocity (since drag ∝ v²).
1 hp = 745.7 W was defined by James Watt as the power of a draft horse turning a mill wheel. In practice, a real horse can sustain about 0.7 hp for extended periods and peak at ~15 hp briefly. A typical human can sustain ~0.1 hp (75 W) and sprint at ~1-2 hp for seconds.
Real machines waste energy as heat, friction, and noise. A motor with 85% efficiency must consume P_input = P_output / 0.85 — about 18% more power than the useful output. The wasted power (15%) becomes heat that may require cooling. Electric motors (85-95% efficient) beat combustion engines (25-40%) dramatically.
A healthy adult can sustain about 75 W (0.1 hp) for hours — that's brisk walking or easy cycling. Elite cyclists sustain 300-400 W. Sprinting produces 1000-2000 W for a few seconds. For comparison, your body's total metabolic power is about 80-100 W at rest, mostly released as heat.
BTU/hr (British Thermal Units per hour) is traditional in HVAC because it directly relates to heat transfer. 1 BTU = energy to heat 1 lb of water by 1°F. A 12,000 BTU/hr air conditioner (1 'ton' of cooling) removes 3,517 W of heat. This unit persists in the US heating/cooling industry.
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