Horsepower (metric) (PS) to Milliwatts (mW) conversion

Horsepower (metric) to Milliwatts conversion table

Horsepower (metric) (PS)	Milliwatts (mW)
0	0
1	735498.75
2	1470997.5
3	2206496.25
4	2941995
5	3677493.75
6	4412992.5
7	5148491.25
8	5883990
9	6619488.75
10	7354987.5
20	14709975
30	22064962.5
40	29419950
50	36774937.5
60	44129925
70	51484912.5
80	58839900
90	66194887.5
100	73549875
1000	735498750

How to convert horsepower (metric) to milliwatts?

Here's a breakdown of how to convert between metric horsepower and milliwatts, focusing on the conversion process and practical examples.

Understanding the Conversion Between Horsepower (metric) and Milliwatts

The conversion between horsepower (metric) and milliwatts involves understanding that both are units of power. Horsepower is a larger unit often used for engines, while milliwatts are much smaller, typically used in electronics. The key is to use the correct conversion factor.

Conversion Formulae

Horsepower (metric) to Milliwatts:

One metric horsepower is equal to 735.49875 watts. Since 1 watt equals 1000 milliwatts:
$1 \text{ hp (metric)} = 735.49875 \text{ W} = 735498.75 \text{ mW}$
Milliwatts to Horsepower (metric):

To convert from milliwatts to horsepower (metric), divide the number of milliwatts by 735498.75:
$1 \text{ mW} = \frac{1}{735498.75} \text{ hp (metric)} \approx 1.36 \times 10^{-6} \text{ hp (metric)}$

Step-by-Step Conversion Instructions

Converting 1 Horsepower (metric) to Milliwatts:

Start with the value in horsepower (metric): 1 hp (metric).
Multiply by the conversion factor: $1 \text{ hp (metric)} \times 735498.75 \frac{\text{mW}}{\text{hp (metric)}}$ .
Result: $735498.75 \text{ mW}$ .

Converting 1 Milliwatt to Horsepower (metric):

Start with the value in milliwatts: 1 mW.
Multiply by the conversion factor: $1 \text{ mW} \times 1.36 \times 10^{-6} \frac{\text{hp (metric)}}{\text{mW}}$ .
Result: Approximately $1.36 \times 10^{-6} \text{ hp (metric)}$ .

Historical Context and Interesting Facts

The concept of horsepower was popularized by James Watt, a Scottish inventor and mechanical engineer, in the late 18th century. He used it to compare the power of steam engines to the power of draft horses.
- James Watt Biography
While Watt defined the imperial horsepower, the metric horsepower ( Pferdestärke (PS) in German, cheval-vapeur (CV) in French, cavallo vapore (cv) in Italian, and paardekracht (pk) in Dutch) is slightly different and equals the power required to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one meter in one second.

Real-World Examples and Quantities

Here are a few examples to illustrate conversions:

Electric Motor: A small electric motor might be rated at 0.1 hp (metric). This is equivalent to $0.1 \text{ hp (metric)} \times 735498.75 \frac{\text{mW}}{\text{hp (metric)}} = 73549.875 \text{ mW}$ .
Solar Panel Output: A small solar panel might generate 500 mW of power, which is equivalent to $500 \text{ mW} \times 1.36 \times 10^{-6} \frac{\text{hp (metric)}}{\text{mW}} = 6.8 \times 10^{-4} \text{ hp (metric)}$ .
Automobile Engine: A car engine may produce 150 hp (metric), which is equal to $150 \text{ hp (metric)} \times 735498.75 \frac{\text{mW}}{\text{hp (metric)}} = 110324812.5 \text{ mW}$ or 110.3248125 kW.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the Milliwatts to other unit conversions.

What is Horsepower (metric)?

This section will provide a comprehensive overview of metric horsepower, including its definition, origins, calculation, and real-world applications.

Definition and Origin

Metric horsepower (PS, PferdeStärke in German, or cheval-vapeur in French) is a unit of power defined as the power required to raise a mass of 75 kilograms against Earth's gravitational force over a distance of one meter in one second. It is slightly less than the imperial horsepower.

Calculation

The value of one metric horsepower is:

1 \text{ PS} = \frac{75 \text{ kg} \cdot 9.80665 \text{ m/s}^2 \cdot 1 \text{ m}}{1 \text{ s}} \approx 735.499 \text{ watts}

Therefore, approximately:

$1 \text{ PS} \approx 0.98632 \text{ hp}$ (Imperial Horsepower)

$1 \text{ hp} \approx 1.01387 \text{ PS}$

Historical Context

The term "horsepower" was originally coined by James Watt to compare the output of steam engines to the power of draft horses. While Watt's original definition is related to the imperial horsepower, the metric horsepower evolved separately on the European continent, primarily for similar comparisons involving machinery and animal power.

Real-World Examples

Automobiles: Engine power is commonly specified in metric horsepower in many parts of the world. For example, a typical family car might have an engine rated at 150 PS.
Motorcycles: Motorcycle engine power is also frequently stated in metric horsepower.
Agricultural Machinery: Tractors and other farming equipment often have their power output measured in PS.
Industrial Pumps and Motors: The power of pumps, fans, and electric motors used in industrial applications can be rated in metric horsepower. For example a pump may be rated at 5 PS.

Fun fact

While not commonly named after any specific person or law, it's interesting to know how metric horsepower is used across Europe. It gives the user a good understanding of the "power" of a machine.

What is Milliwatts?

Milliwatts are a unit of power, commonly used to measure small amounts of electrical or other forms of power. Understanding milliwatts helps in various applications from electronics to radio communication.

Milliwatts Defined

A milliwatt (mW) is a unit of power in the International System of Units (SI). It is equal to one-thousandth (1/1000) of a watt. Since a watt is a joule per second, a milliwatt represents 0.001 joules of energy being converted or consumed per second.

Mathematically:

$1 mW = \frac{1}{1000} W = 0.001 W$

How Milliwatts Are Formed

The term "milliwatt" is derived from the SI prefix "milli-", which denotes a factor of $10^{-3}$ or 1/1000, combined with the unit of power, the watt (W). The watt, in turn, is named after James Watt, a Scottish inventor and mechanical engineer known for his improvements to the steam engine.

Real-World Examples of Milliwatts

Milliwatts are commonly encountered in situations involving low power consumption:

Small Electronic Devices: Many portable electronic devices like headphones, smartwatches, and sensors operate in the milliwatt range to conserve battery life.
Laser Pointers: The output power of laser pointers is often limited to a few milliwatts to ensure safety.
Radio Transmitters: Low-power radio transmitters, such as those used in wireless sensor networks or short-range communication devices, may have output powers measured in milliwatts.
Hearing Aids: Hearing aids consume very little power, typically measured in milliwatts.
Medical Devices: Certain medical devices, like implanted sensors, use milliwatts of power for operation.

Power Calculations & Conversions

Understanding the relationship between milliwatts, volts, and amps is crucial in electronics. Power (P) in watts can be calculated using the following formulas:

$P = VI$ (where V is voltage in volts and I is current in amperes)
$P = I^2R$ (where I is current in amperes and R is resistance in ohms)
$P = \frac{V^2}{R}$ (where V is voltage in volts and R is resistance in ohms)

To convert from watts to milliwatts, multiply by 1000. To convert from milliwatts to watts, divide by 1000.

For example, if a device operates at 5 volts and draws 0.1 amperes of current, the power consumption is:

$P = 5V * 0.1A = 0.5 W = 500 mW$

James Watt and the Development of Power Measurement

While milliwatts are a modern unit, they're directly related to the watt, named after James Watt. Watt's improvements to the steam engine were pivotal in the Industrial Revolution. He also developed the concept of horsepower as a unit of power, which later led to the standardization of the watt as the SI unit of power.

Read more about James Watt and the History of the Watt in britannica

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Power consumption
Electrical power
Wattage
Voltage
Current
Energy efficiency
SI units
Electronics
mW to W conversion

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Complete Horsepower (metric) conversion table

Enter # of Horsepower (metric)

Convert 1 PS to other units	Result
Horsepower (metric) to Watts (PS to W)	735.49875
Horsepower (metric) to Milliwatts (PS to mW)	735498.75
Horsepower (metric) to Kilowatts (PS to kW)	0.73549875
Horsepower (metric) to Megawatts (PS to MW)	0.00073549875
Horsepower (metric) to Gigawatts (PS to GW)	7.3549875e-7
Horsepower (metric) to British thermal units per second (PS to Btu/s)	0.6971182104441
Horsepower (metric) to Foot-pounds per second (PS to ft-lb/s)	542.47603863681
Horsepower (metric) to Horsepower (British) (PS to hp)	0.9863200702488