# Power converter

> Convert hp to kW, kW to hp, watts to horsepower and BTU/h to tons of refrigeration, with mechanical (745.7 W) and metric (735.5 W) horsepower.

Interactive version: https://www.calcopenly.com/conversion/power-converter
Subject: Unit converters

Every power unit is a fixed number of watts (joules per second). Mechanical horsepower is 550 foot-pounds-force per second, which works out at exactly 745.69987158227022 W; metric horsepower (PS) is 75 kilogram-force metres per second, exactly 735.49875 W. A ton of refrigeration is 12,000 BTU/h, about 3.517 kW.

The default converts a 100 hp engine to 74.57 kW. Car specifications are the usual reason: European registration documents give engine power in kW while brochures quote PS or hp, and 100 kW is 134.1 hp or 136.0 PS.

Air-conditioner ratings in BTU/h or tons describe cooling output, not the electricity drawn: a 1.5-ton unit moves 18,000 BTU/h (5.28 kW) of heat, and its electrical input depends on its efficiency rating.

## Inputs

- **Value**: A number in the “from” unit, or with its own unit
- **From** (options: watt (W), milliwatt (mW), kilowatt (kW), megawatt (MW), gigawatt (GW), horsepower (hp), metric horsepower (PS), BTU per hour (BTU/h), ton of refrigeration (TR), kilocalorie per hour (kcal/h))
- **To** (options: watt (W), milliwatt (mW), kilowatt (kW), megawatt (MW), gigawatt (GW), horsepower (hp), metric horsepower (PS), BTU per hour (BTU/h), ton of refrigeration (TR), kilocalorie per hour (kcal/h))

## Results

- Converted value — main result
- Conversion
- Conversion factor
- Exactness

## Formula

$$
\begin{gathered} x_{\text{to}} = x_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \\ f = \text{one unit expressed in } \text{W} \end{gathered}
$$

## Worked examples

### 100 hp in kW

- Value: 100 hp
- From: horsepower (hp)
- To: kilowatt (kW)
- **Converted value: 74.5699871582 kW**
- **Exactness: Exact**
- Checked against: 1 hp = 550 ft·lbf/s = 550 × 0.3048 × 4.4482216152605 W = 745.69987158227022 W (NIST SP 811 App. B)

### 1 kW in hp

- Value: 1 kW
- From: kilowatt (kW)
- To: horsepower (hp)
- **Converted value: 1.3410220896 hp**
- Checked against: 1000 / 745.69987158227022 (Python 3.8 fractions from the legal definitions)

### 12,000 BTU/h is one ton of refrigeration

- Value: 12,000 BTU/h
- From: BTU per hour (BTU/h)
- To: ton of refrigeration (TR)
- **Converted value: 1 TR**
- Checked against: 1 ton of refrigeration = 12,000 BTU/h (NIST SP 811 App. B)

### Zero power

- Value: 0 W
- From: watt (W)
- To: horsepower (hp)
- **Converted value: 0 hp**
- **Exactness: Exact**
- Checked against: 0 × any factor = 0

### 1 metric horsepower in watts

- Value: 1 PS
- From: metric horsepower (PS)
- To: watt (W)
- **Converted value: 735.49875 W**
- Checked against: 1 PS = 75 kgf·m/s = 75 × 9.80665 W = 735.49875 W

## Questions

### How many watts are in a horsepower?

745.7 W for mechanical horsepower (550 ft·lbf/s), 735.5 W for metric horsepower (PS or CV), and exactly 746 W for the electric horsepower used to rate electric motors; NIST SP 811 lists all three. Mechanical and metric horsepower differ by 1.4%, enough to matter when comparing car figures.

### How do I convert kW to hp?

Multiply by 1.34102 for mechanical horsepower or by 1.35962 for metric PS. A 150 kW engine is 201.2 hp or 203.9 PS. To go from hp to kW, multiply by 0.7457, so the default 100 hp is 74.57 kW.

### What is the difference between hp, bhp and PS?

hp and bhp use the same 745.7 W unit; “brake” horsepower means the power was measured at the engine's output shaft, before transmission losses. PS (Pferdestärke) is metric horsepower, 735.5 W, also written CV or ch. A car quoted at 150 PS makes 147.9 hp or 110.3 kW.

### What does a 1.5-ton air conditioner mean?

It removes 18,000 BTU of heat per hour, which is 5.28 kW of cooling. A ton of refrigeration is 12,000 BTU/h, the rate that melts one short ton (2,000 lb) of ice in 24 hours, because ice absorbs 144 BTU per pound as it melts. The electricity it draws is lower and depends on its efficiency rating.

### How many BTU/h is 1 kW?

3,412.14 BTU/h. One watt is 3.41214 BTU/h, so a 2 kW electric heater gives out 6,824 BTU/h, and a 12,000 BTU/h air conditioner is rated at 3.517 kW of cooling. The factor is the same as between kWh and BTU because both sides are divided by one hour.

### How accurate is the power converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “100 hp in kW” is checked against 1 hp = 550 ft·lbf/s = 550 × 0.3048 × 4.4482216152605 W = 745.69987158227022 W (NIST SP 811 App. B).

### Where does the method come from?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement.

## Sources

- [NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44, Appendix C — General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)