Foot-pounds per second (ft-lb/s) to Horsepower (metric) (PS) conversion

Converting between foot-pounds per second and metric horsepower is a common task in engineering and physics. Here's how to convert between these two units of power.

Understanding the Conversion

Power is the rate at which work is done or energy is transferred. Foot-pounds per second (ft⋅lb/s) is an imperial unit of power, while metric horsepower (PS or Pferdestärke) is a metric unit. One metric horsepower is defined as the power required to lift a mass of 75 kilograms against Earth's gravity over a distance of one meter in one second.

Conversion Formulas

• Foot-pounds per second to Metric Horsepower:

  $$1 \, \text{ft⋅lb/s} = \frac{1}{542.48} \, \text{PS} \approx 0.001843 \, \text{PS}$$

• Metric Horsepower to Foot-pounds per second:

  $$1 \, \text{PS} = 542.48 \, \text{ft⋅lb/s}$$

Step-by-Step Conversion Instructions

Converting 1 ft⋅lb/s to Metric Horsepower:

1. Use the conversion factor: $1 \, \text{ft⋅lb/s} \approx 0.001843 \, \text{PS}$.

2. Multiply 1 ft⋅lb/s by the conversion factor:

   $$1 \, \text{ft⋅lb/s} \times 0.001843 \, \text{PS/ft⋅lb/s} = 0.001843 \, \text{PS}$$

   Therefore, 1 foot-pound per second is approximately 0.001843 metric horsepower.

Converting 1 Metric Horsepower to Foot-pounds per second:

1. Use the conversion factor: $1 \, \text{PS} = 542.48 \, \text{ft⋅lb/s}$.

2. Multiply 1 PS by the conversion factor:

   $$1 \, \text{PS} \times 542.48 \, \text{ft⋅lb/s/PS} = 542.48 \, \text{ft⋅lb/s}$$

   Therefore, 1 metric horsepower is equal to 542.48 foot-pounds per second.

Historical Context and Notable Figures

The concept of horsepower was popularized by James Watt, a Scottish inventor and mechanical engineer, to compare the power of steam engines to the power of draft horses. Although Watt defined Imperial Horsepower (approximately 745.7 watts), the metric horsepower is slightly different (approximately 735.5 watts).

Real-World Examples

1. Small Electric Motor:
   • A small electric motor might produce around 100 ft⋅lb/s. Converting this to metric horsepower:

     $$100 \, \text{ft⋅lb/s} \times 0.001843 \, \text{PS/ft⋅lb/s} = 0.1843 \, \text{PS}$$

2. Automobile Engine:
   • An engine producing 200 metric horsepower is equivalent to:

     $$200 \, \text{PS} \times 542.48 \, \text{ft⋅lb/s/PS} = 108496 \, \text{ft⋅lb/s}$$

3. Industrial Pump:
   • An industrial pump might require 2500 ft⋅lb/s to operate. In metric horsepower:

     $$2500 \, \text{ft⋅lb/s} \times 0.001843 \, \text{PS/ft⋅lb/s} = 4.6075 \, \text{PS}$$

External Links

• NIST - Guide for the Use of the International System of Units (SI)

How to Convert Foot-pounds per second to Horsepower (metric)

To convert Foot-pounds per second (ft-lb/s) to Horsepower (metric) (PS), multiply the power value by the conversion factor between these two units. For this conversion, the factor is $1\ \text{ft-lb/s} = 0.001843399392373\ \text{PS}$.

1. Write the conversion factor:
   Use the known relationship between the units:

   $$1\ \text{ft-lb/s} = 0.001843399392373\ \text{PS}$$

2. Set up the conversion formula:
   Multiply the given value in ft-lb/s by the conversion factor:

   $$\text{PS} = \text{ft-lb/s} \times 0.001843399392373$$

3. Substitute the given value:
   Insert $25$ for the Foot-pounds per second value:

   $$\text{PS} = 25 \times 0.001843399392373$$

4. Calculate the result:
   Perform the multiplication:

   $$\text{PS} = 0.04608498480932$$

5. Result:

   $$25\ \text{Foot-pounds per second} = 0.04608498480932\ \text{Horsepower (metric)}$$

A quick way to check your work is to make sure the result is much smaller than 1 PS, since 25 ft-lb/s is a relatively small power value. Keeping the unit label as PS helps avoid confusion with mechanical horsepower.

What is the formula to convert Foot-pounds per second to Horsepower (metric)?

To convert Foot-pounds per second to Horsepower (metric), multiply the value in ft-lb/s by the verified factor $0.001843399392373$. The formula is: $PS = \text{ft-lb/s} \times 0.001843399392373$. This gives the equivalent power in metric horsepower.

How many Horsepower (metric) are in 1 Foot-pound per second?

There are $0.001843399392373$ Horsepower (metric) in $1$ Foot-pound per second. This is the direct conversion factor used for all ft-lb/s to PS calculations.

Why is the conversion factor from Foot-pounds per second to Horsepower (metric) so small?

A Foot-pound per second is a relatively small unit of power compared with Horsepower (metric). Since $1$ ft-lb/s equals only $0.001843399392373$ PS, it takes many ft-lb/s to make up one metric horsepower. This is why the converted value is usually much smaller in PS.

Where is converting Foot-pounds per second to Horsepower (metric) used in real life?

This conversion is useful in engineering, mechanics, and machinery performance comparisons. For example, older technical documents or specialized systems may express power in ft-lb/s, while automotive and industrial contexts may prefer PS. Converting between them helps keep measurements consistent across standards.

Can I convert Horsepower (metric) back to Foot-pounds per second?

Yes, you can reverse the conversion by dividing the value in PS by $0.001843399392373$. This gives the corresponding value in Foot-pounds per second. Using the same verified factor ensures consistency in both directions.

Is Horsepower (metric) the same as mechanical horsepower?

No, Horsepower (metric) and mechanical horsepower are different units, even though both measure power. On this page, the target unit is specifically Horsepower (metric), abbreviated as $PS$. Using the verified factor $1\ \text{ft-lb/s} = 0.001843399392373\ PS$ ensures the correct metric-horsepower conversion.