Power Converter

Accurate power measurements are essential for engineers, electricians, and students working in electrical systems. Whether you are designing motors, analyzing energy efficiency, or comparing mechanical and electrical outputs, understanding how power is expressed and converted helps avoid costly mistakes and ensures optimal performance across diverse applications.

Power Converter User Interface — Our power converter interface enables instant and bidirectional power unit conversion.

Our power converter interface enables instant and bidirectional power unit conversion. It streamlines the process by facilitating quick conversions between watts, kilowatts, horsepower, and other units. Before diving into conversions, let’s explore the core concepts.

Definitions

Let's begin by clarifying the definitions and differences between power, watts, and horsepower. Understanding these concepts will enable you to perform conversions with confidence.

What is Power?

Power is the rate at which work is done or energy is transferred over time. In electrical systems, it represents how quickly electrical energy is consumed or produced.^[1]

Mathematically, power is expressed as:

$$\boxed{P = \frac{W}{t}}$$

Where:

P is power in watts (W)
W is work or energy in joules (J)
t is time in seconds (s)

What is Watt?

Watt (W) is the SI derived unit of power, named after James Watt, the Scottish engineer who improved the steam engine. It measures the rate of energy transfer per unit time.^[1]

Mathematically 1 W = 1 j/s:

$$\boxed{1 \,\text{Watt} = 1 \,\frac{\text{Joule}}{\text{Second}}}$$

Where:

j = joule unit of energy
s = second unit of time

Thus, one watt equals one joule of energy transferred every second.

What is Horsepower?

Horsepower (hp) is a non-SI unit of power historically developed by James Watt to compare steam engine output to the work of draft horses. It remains widely used in mechanical and automotive contexts.^[2]

Horsepower provides a practical measure for engines, motors, and turbines, bridging mechanical and electrical power comparisons.

There are four common types of horsepower, each defined for specific applications.^[3]

Mechanical horsepower: Used in the U.S. for engines and motors. Defined by James Watt as 550 ft·lbf/s.
Metric horsepower: Used in Europe and Asia. Based on lifting 75 kg over 1 meter in 1 second.
Electrical horsepower: Used for electric motors. Exactly defined as 746 watts.
Boiler horsepower: Measures steam boiler output. Based on the energy to evaporate 34.5 lb of water/hr.

Here are their symbols, short symbols (used in our calculator), and their values in watts.

Type	Symbol	Short	Value (W)
Mechanical horsepower	hp (imperial)	hp	745.7 W
Metric horsepower	PS / cv / hk	hpM	735.5 W
Electrical horsepower	hp (electric)	hpE	746 W
Boiler horsepower	hp (boiler)	bhp	9,809.5 W

Comparison of common horsepower types, including mechanical, metric, electrical, and boiler horsepower, with their standardized watt equivalents and symbols used across engineering and automotive contexts.

SI Units of Power

The SI (International System of Units) unit system^[4] follows a decimal-based structure, where each unit is a multiple or fraction of 10 (10⁰, 10¹, 10², etc.). The table below lists the standard SI prefixes for watt, along with their symbols, multipliers, and names.

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10⁻¹ W	dW	deciwatt	10¹ W	daW	decawatt
10⁻² W	cW	centiwatt	10² W	hW	hectowatt
10⁻³ W	mW	milliwatt	10³ W	kW	kilowatt
10⁻⁶ W	μW	microwatt	10⁶ W	MW	megawatt
10⁻⁹ W	nW	nanowatt	10⁹ W	GW	gigawatt
10⁻¹² W	pW	picowatt	10¹² W	TW	terawatt
10⁻¹⁵ W	fW	femtowatt	10¹⁵ W	PW	petawatt
10⁻¹⁸ W	aW	attowatt	10¹⁸ W	EW	exawatt
10⁻²¹ W	zW	zeptowatt	10²¹ W	ZW	zettawatt
10⁻²⁴ W	yW	yoctowatt	10²⁴ W	YW	yottawatt
10⁻²⁷ W	rW	rontowatt	10²⁷ W	RW	ronnawatt
10⁻³⁰ W	qW	quectowatt	10³⁰ W	QW	quettawatt

SI prefixes applied to the watt (W), ranging from quectowatt to quettawatt, covering both submultiples and multiples used in scientific, engineering, and power system contexts.

These prefixes help simplify electric power measurements across a wide range of applications, from microelectronics to high-power systems.

Non-SI Units of Power

In addition to the watt (W), several non-SI units are used across mechanical, thermal, and historical contexts. These units are standardized for conversion and remain relevant in specific industries such as HVAC, automotive, and thermodynamics.

Unit Name	Symbol(s)	Value (W)	Description
Mechanical horsepower	hp (imperial)	745.7 W	U.S. standard for engine output. Defined as 550 ft·lbf/s.
Metric horsepower	PS / cv / hk	735.5 W	Used in Europe and Asia. Based on lifting 75 kg·m/s.
Electrical horsepower	hp (electric)	746 W	Defined exactly as 746 watts for electric motors.
Boiler horsepower	bhp	9,809.5 W	Steam boiler rating. Based on evaporating 34.5 lb of water/hr.
Hydraulic horsepower	hp (hydraulic)	~745.7 W	Power from fluid flow and pressure.
BTU per hour	BTU/h	0.29307107 W	Common in HVAC systems. 1 BTU = heat to raise 1 lb of water by 1°F.
Calorie per second	cal/s	4.1868 W	Used in thermodynamics. 1 cal = 4.1868 J.
Kilocalorie per hour	kcal/h	1.162222 W	Often used in metabolic and heating contexts.
Foot-pound per second	ft·lbf/s	1.3558179 W	British engineering unit.
Erg per second	erg/s	1×10⁻⁷ W	CGS unit of power. 1 erg = 1×10⁻⁷ J.

Comparison of non-SI power units including mechanical, thermal, and historical measures, with their precise watt equivalents and contextual usage across engineering, HVAC, and scientific domains.

Power Unit Conversion Table

The table below provides a quick reference for converting commonly used capacitance units, ranging from farads to picofarads, to help you perform conversions efficiently.

From	Watt (W)	Milliwatt (mW)	Kilowatt (kW)	Megawatt (MW)	Electrical Horsepower (hpE)	BTU/h	Calorie/s (cal/s)	Erg/s
1 W =	1 W	1,000 mW	0.001 kW	0.000001 MW	0.00134048 hpE	3.41214 BTU/h	0.239006 cal/s	10,000,000 erg/s
1 mW =	0.001 W	1 mW	0.000001 kW	0.000000001 MW	0.00000134048 hpE	0.003412 BTU/h	0.000239 cal/s	10,000 erg/s
1 kW =	1,000 W	1,000,000 mW	1 kW	0.001 MW	1.34048 hpE	3,412.14 BTU/h	239.006 cal/s	10,000,000,000 erg/s
1 MW =	1,000,000 W	1,000,000,000 mW	1,000 kW	1 MW	1,340.48 hpE	3,412,140 BTU/h	239,006 cal/s	10,000,000,000,000 erg/s
1 hpE =	746 W	746,000 mW	0.746 kW	0.000746 MW	1 hpE	2,547.52 BTU/h	178.27 cal/s	7,460,000,000 erg/s
1 BTU/h =	0.29307107 W	293.07107 mW	0.000293 kW	2.93071×10⁻⁷ MW	0.000392 hpE	1 BTU/h	0.07003 cal/s	2,930,710 erg/s
1 cal/s =	4.1868 W	4,186.8 mW	0.0041868 kW	0.00000419 MW	0.00561 hpE	14.2857 BTU/h	1 cal/s	41,868,000 erg/s
1 erg/s =	1×10⁻⁷ W	0.0001 mW	1×10⁻¹⁰ kW	1×10⁻¹³ MW	1.34048×10⁻¹⁰ hpE	3.412×10⁻⁷ BTU/h	2.390×10⁻⁸ cal/s	1 erg/s

Conversion matrix for selected SI and non-SI power units including watt, milliwatt, kilowatt, megawatt, electrical horsepower, BTU per hour, calorie per second, and erg per second.

Examples

The following examples demonstrate how to convert between different capacitance units, helping you apply these calculations in practical scenarios.

Example 1: Converting SI Power Units in Solar Panel Design

In solar panel design, engineers often calculate power output in kilowatts (kW) but need to convert it to watts (W) for component-level analysis. Suppose a solar array generates 3.5 kW during peak sunlight. To evaluate inverter compatibility, you must convert this to watts.

Solution

Since 1 kilowatt (kW) = 1,000 watts (W), we can convert 3.5 kW to watt using the following formula:

$$\text{P}_\text{(W)} = \text{P}_\text{(kW)} \times 1{,}000$$

$$\text{P}_\text{(W)} = 3.5 \times 1{,}000 = \boxed{3{,}500 \text{ W}}$$

Therefore, 3.5 kW electric power is equivalent to 3,500 W.

To solve the problem with our calculator, follow the steps below:

Select the "From" unit: Choose kW = Kilowatt from the dropdown menu.
Select the "To" unit: Choose W = Watt from the dropdown menu.
Enter the value in kilowatt: For this example, enter 3.5 into the From box.
View the result: The converter instantly calculates and displays the equivalent value in watts: 3,500 W.

Power Converter Example 2 - Converting from kW to W — Steps to convert from kilowatts to watts with our power converter

Example 2: Converting Non-SI Power Units in HVAC System Analysis

In HVAC systems, thermal output is often rated in BTU/h. Suppose a heater is rated at 10,000 BTU/h, and you want to convert this to watts (W) for energy efficiency calculations.

Solution

Since 1 BTU/h = 0.29307107 watts (W), we can convert 10,000 BTU/h to watt using the following formula:

$$\text{P}_\text{(W)} = \text{P}_\text{(BTU/h)} \times 0.29307107$$

$$\text{P}_\text{(W)} = 10{,}000 \times 0.29307107 = \boxed{2{,}930.71 \text{ W}}$$

Therefore, 10,000 BTU/h heating power is equivalent to 2,930.71 W.

To solve the problem with our calculator, follow the steps below:

Select the "From" unit: Choose BTU/h = BTU per hour from the dropdown menu.
Select the "To" unit: Choose W = Watt from the dropdown menu.
Enter the value in BTU/h: For this example, enter 10,000 into the From box.
View the result: The converter instantly calculates and displays the equivalent value in watts: 2,930.7107 W.

Power Converter Example 2 - Converting from BTU/s to W — Steps to convert from BTU/h to watts with our power converter

You have learned how to convert between power units. You can now efficiently use our calculator to convert power measurement units, saving time on future calculations.

Definitions

SI Units of Power

Non-SI Units of Power

Power Unit Conversion Table

Examples

About this app

References