How do I convert horsepower to kilowatts?

Multiply by 0.745699. 1 hp = 745.699 W = 0.7457 kW. Example: 200 hp = 149.1 kW. Reverse: 1 kW = 1.34102 hp.

How do I convert kilowatts to horsepower?

Multiply by 1.34102. 1 kW = 1.34102 hp (mechanical). Example: 150 kW = 201 hp.

What is a ton of refrigeration in kW?

1 ton of refrigeration = 12,000 BTU/h = 3.51685 kW. It is the cooling capacity, not input electrical power.

What is the difference between mechanical and metric horsepower?

Mechanical hp (SAE): 745.699 W. Metric hp (PS/DIN): 735.499 W. Difference: 1.35%. US spec sheets use mechanical hp; European use PS.

⚡ Power Conversion Calculator

Convert between watts, kW, MW, horsepower, BTU/h, kVA, tons of refrigeration and 25+ units — with Ohm's law, power factor, mechanical & thermal power formulas rendered in MathJax

25+ Units SI · Mechanical · Thermal kW ↔ HP · kW ↔ BTU Free & Instant

🔄 Power Unit Converter

Enter Value From Unit

Result To Unit

1 kW = 1.34102 hp

Formula: value × 1.34102

⚡ All Units at Once

💡 Definition: Power = rate of energy transfer: $ P = \dfrac{W}{t} = \dfrac{\text{Energy (J)}}{\text{Time (s)}} $ — all units convert through the watt (W = J/s) as the SI pivot.

📖 How to Use This Power Conversion Calculator

1

Filter by Unit Category (Optional)
Click SI (Watts), Mechanical, or Thermal to narrow the dropdowns. "All Units" shows all 27 supported units together. Mechanical includes horsepower variants and torque-based units; Thermal covers BTU/h, tons of refrigeration, and calories.
2

Enter Your Power Value
Type the value into "Enter Value." Decimals, very small (mW, µW) and very large (GW, TW) values are all fully supported with automatic scientific notation display.
3

Select From and To Units
Choose your source unit from "From Unit" and target from "To Unit." The result appears instantly with the exact multiplication factor for manual verification.
4

Use Quick-Convert Buttons
Click kW→hp, hp→kW, kW→BTU/h, BTU/h→W, kW→Tons, or MW→kW for the most common power conversions. Both dropdowns set automatically — no manual unit selection needed.
5

View All Units & Copy
The "All Units at Once" panel shows your power value in every supported unit simultaneously. Click "📋 Copy Result" to copy the primary conversion to clipboard for reports or datasheets.

📐 Power Unit Conversion Factors Reference

From	To	Multiply By	Math Expression
1 kilowatt (kW)	horsepower (hp)	1.34102	$ 1\,\text{kW} = 1.34102\,\text{hp} $
1 horsepower (hp)	kilowatt (kW)	0.745699	$ 1\,\text{hp} = 745.699\,\text{W} = 0.7457\,\text{kW} $
1 watt (W)	kW	0.001	$ 1\,\text{W} = 10^{-3}\,\text{kW} = 1\,\text{J/s} $
1 kW	MW	0.001	$ 1\,\text{kW} = 10^{-3}\,\text{MW} $
1 kW	BTU/hour	3,412.14	$ 1\,\text{kW} = 3{,}412.14\,\text{BTU/h} $
1 BTU/hour	watt	0.29307	$ 1\,\text{BTU/h} = 0.29307\,\text{W} $
1 ton of refrigeration	kW	3.51685	$ 1\,\text{TR} = 12{,}000\,\text{BTU/h} = 3.517\,\text{kW} $
1 metric hp (PS)	watt	735.499	$ 1\,\text{PS} = 735.499\,\text{W} $
1 kW	kcal/h	859.845	$ 1\,\text{kW} = 859.845\,\text{kcal/h} $
1 ft·lb/s	watt	1.35582	$ 1\,\text{ft·lb/s} = 1.35582\,\text{W} $

⚡ Understanding Power — A Complete Engineering Guide

Power is the rate at which energy is transferred, converted, or consumed. It is the single most critical quantity in electrical engineering, mechanical design, thermodynamics, and every energy system from a smartphone battery to a nuclear power plant. Despite this centrality, power is measured in an extraordinary range of units — watts in SI science, horsepower in automotive engineering, BTU/hour in HVAC and heating, kilowatt-hours in electricity billing, and tons of refrigeration in cooling systems — each arising from a distinct historical and industrial tradition.

Understanding how to convert between these unit systems accurately is essential for engineers, electricians, HVAC technicians, automotive designers, data centre managers, and anyone calculating energy costs, motor sizing, or heat loads. A misplaced decimal in a kW-to-BTU/h conversion can result in undersized heating equipment; a confused kW-to-hp ratio can lead to motor overload. This guide clarifies every major power unit, provides all key conversion formulas in mathematical notation, and gives real-world context for each.

Power — Fundamental SI Definition

\[ P = \frac{W}{t} = \frac{dE}{dt} \]

$P$ = power (W = J/s) · $W$ = work done (J) · $t$ = time (s) · $dE/dt$ = instantaneous rate of energy transfer · SI unit: watt (W) — named after James Watt (1736–1819)

💡 The Watt — SI Unit of Power

The watt (W) was adopted as the SI unit of power in 1960, honouring James Watt whose steam engine innovations directly catalysed the Industrial Revolution. One watt is defined as one joule of energy transferred per second — an extraordinarily small but precisely defined unit. To put it in perspective: a single LED bulb (~10 W) consumes 10 joules every second; a standard electric kettle (~2,000 W) consumes 2,000 joules per second; the total power of global human civilisation is approximately 18 terawatts (18 × 10¹² W).

SI Power Scale — Watt Prefixes

$ 1\,\text{W} = 1\,\text{J/s} = 1\,\text{kg·m}^2\text{/s}^3 \quad \text{(SI definition)} $

$ 1\,\text{kW} = 10^3\,\text{W} \qquad \text{(household appliances, small motors)} $

$ 1\,\text{MW} = 10^6\,\text{W} \qquad \text{(power stations, large industrial)} $

$ 1\,\text{GW} = 10^9\,\text{W} \qquad \text{(large power plants, national grids)} $

$ 1\,\text{TW} = 10^{12}\,\text{W} \qquad \text{(global civilisation energy scales)} $

Reverse: $1\,\text{kWh} = 3{,}600{,}000\,\text{J}$ (kilowatt-hour — the billing unit of electrical energy, not power)

🐎 Horsepower — Mechanical Power & the HP→kW Conversion

Horsepower (hp) was defined by James Watt himself in the 1780s to market his steam engines against horses — the dominant power source of the era. Watt observed a mill horse working at a rate he estimated as approximately 33,000 foot-pounds of work per minute, and used this as his marketing benchmark. This definition became mechanical horsepower, and despite being a purely historical artefact, it remains the dominant power unit in US and UK automotive and industrial contexts today.

There are actually four distinct horsepower definitions in current use, each with slightly different watt equivalents:

Mechanical (imperial) hp: 550 ft·lbf/s = 745.69987 W (SAE standard in US automotive)
Metric hp (PS, CV, ch, pk): 75 kgf·m/s = 735.49875 W (DIN standard in European automotive)
Electrical hp: Exactly 746 W (US electrical motor ratings)
Boiler hp: 33,475 BTU/h = 9,809.5 W (steam engineering legacy)

Horsepower Conversions — All Four Definitions

$ 1\,\text{hp}_{\text{mech}} = 550\,\text{ft·lbf/s} = 745.699\,\text{W} \approx 0.7457\,\text{kW} $

$ 1\,\text{PS}_{\text{metric}} = 75\,\text{kgf·m/s} = 735.499\,\text{W} \approx 0.7355\,\text{kW} $

$ 1\,\text{hp}_{\text{elec}} = 746\,\text{W} \quad \text{(exact, for electric motor nameplate ratings)} $

$ 1\,\text{kW} = \frac{1000}{745.699}\,\text{hp}_{\text{mech}} = 1.34102\,\text{hp} $

Always specify which HP definition — using metric PS instead of mechanical hp introduces a 1.35% error, which matters for engine dyno comparison, EV spec sheets, and international certification

📌 Worked Example — Electric Vehicle kW to HP Comparison

Problem: A Tesla Model 3 Long Range is rated at 358 kW. What is this in mechanical horsepower and metric PS?

Step 1 — kW to mechanical hp: $ 358\,\text{kW} \times 1.34102 = 480.1\,\text{hp}_{\text{mech}} $

Step 2 — kW to metric PS: $ 358{,}000\,\text{W} \div 735.499 = 486.7\,\text{PS} $

Answer: 358 kW = 480 hp (SAE mechanical, US spec sheet) = 487 PS (DIN metric, European spec). The ~1.4% difference between mechanical hp and metric PS is why US and European car horsepower figures differ slightly for the same vehicle.

🔧 Mechanical Power — Torque, Speed & Angular Velocity

In mechanical engineering, power is not delivered as a raw force — it is always the product of a force and the velocity at which it acts. For rotating systems (motors, engines, turbines, gearboxes), this translates to the product of torque and angular velocity. This relationship is fundamental to every motor sizing calculation, drivetrain design, and engine dyno measurement.

Mechanical Power — Rotational Systems

\[ P = \tau \cdot \omega = \frac{2\pi \cdot N \cdot T}{60} \]

$\tau$ = torque (N·m) · $\omega$ = angular velocity (rad/s) · $N$ = rotational speed (RPM) · $T$ = torque (N·m) · Result: $P$ in watts · Divide by 1000 for kW, by 745.7 for hp

📌 Worked Example — Engine Power from Torque and RPM

Problem: An engine produces peak torque of 350 N·m at 4,500 RPM. Calculate the power in kW and hp.

\[ P = \frac{2\pi \times 4500 \times 350}{60} = \frac{2 \times 3.14159 \times 4500 \times 350}{60} = \frac{9{,}896{,}017}{60} = 164{,}934\,\text{W} \approx \mathbf{164.9\,\text{kW}} \]

In horsepower: $ 164.9\,\text{kW} \times 1.34102 = \mathbf{221.2\,\text{hp}} $

Verify: A 165 kW / 221 hp car at 350 N·m torque peak is consistent with a medium-performance 2.0L turbocharged engine — e.g., comparable to a Ford Focus ST or Volkswagen Golf GTI.

🔌 Electrical Power — Ohm's Law, kW, kVA & Power Factor

In electrical engineering, power takes three distinct forms that are easily confused but critically different: real power (P), apparent power (S), and reactive power (Q). Understanding their relationships is essential for generator sizing, transformer specification, and electrical safety.

Electrical Power Formulas — DC and AC Systems

$ P_{\text{DC}} = V \times I \qquad \text{(DC: direct product of voltage × current)} $

$ P_{\text{AC}} = V \times I \times \cos\phi = S \times \text{PF} \qquad \text{(AC single-phase)} $

$ P_{\text{3\phi}} = \sqrt{3} \times V_L \times I_L \times \cos\phi \qquad \text{(AC three-phase)} $

$ S = V \times I \quad \text{(kVA)} \qquad Q = S\sin\phi \quad \text{(kVAR)} \qquad P = S\cos\phi \quad \text{(kW)} $

$ S^2 = P^2 + Q^2 \qquad \text{(power triangle — Pythagorean relationship)} $

$V$ = voltage (V) · $I$ = current (A) · $\cos\phi$ = power factor (PF, 0–1) · $V_L$ = line voltage · $I_L$ = line current

⚡

Real Power (kW)

Actual work done — lights lit, motors turning, heat generated. Measured by your electricity meter. $P = S \times \text{PF}$. A resistive load (heater, incandescent bulb) has PF = 1.0, so kW = kVA exactly.

📐

Apparent Power (kVA)

Total power supplied — the "gross" power the generator/transformer must provide. $S = V \times I$. Generator and transformer ratings are always in kVA because they must supply reactive current too, even if it does no work.

🔄

Reactive Power (kVAR)

Power that oscillates back and forth without doing useful work — caused by inductors (motors, transformers) and capacitors. $Q = S\sin\phi$. Power factor correction capacitor banks are installed to minimise kVAR and improve efficiency.

🎯

Power Factor (PF)

$\text{PF} = \cos\phi = P/S$. Unity PF (1.0) = fully efficient, all power does work. Motors: 0.7–0.9. Typical commercial building: 0.8–0.95. Low PF wastes capacity and incurs utility penalties.

📌 Worked Example — Generator Sizing (kVA to kW)

Problem: A factory needs 80 kW of real power. The load has a power factor of 0.8. What generator kVA rating is required?

\[ S = \frac{P}{\text{PF}} = \frac{80\,\text{kW}}{0.8} = \mathbf{100\,\text{kVA}} \]

Reactive power: $ Q = \sqrt{S^2 - P^2} = \sqrt{100^2 - 80^2} = \sqrt{10{,}000 - 6{,}400} = \sqrt{3{,}600} = 60\,\text{kVAR} $

Answer: A 100 kVA generator is required to deliver 80 kW of real load at 0.8 PF. Selecting a 80 kVA generator would result in overload. This is why generator specs are always in kVA, not kW.

🔥 Thermal Power — BTU/h, Tons of Refrigeration & HVAC

Thermal power units dominate HVAC engineering, industrial process heating, refrigeration system design, and building energy management. The British Thermal Unit per hour (BTU/h) and the ton of refrigeration are the two most widely used — primarily in the United States but with global industry presence. Converting between these thermal units and electrical watts/kilowatts is a daily task for mechanical and HVAC engineers.

Thermal Power — Key Definitions & Conversion Formulas

$ 1\,\text{BTU/h} = 0.293071\,\text{W} \qquad 1\,\text{kW} = 3{,}412.14\,\text{BTU/h} $

$ 1\,\text{ton of refrigeration} = 12{,}000\,\text{BTU/h} = 3{,}516.85\,\text{W} = 3.517\,\text{kW} $

$ 1\,\text{kcal/h} = 1.163\,\text{W} \qquad 1\,\text{kW} = 859.845\,\text{kcal/h} $

$ \text{COP}_{\text{cooling}} = \frac{Q_{\text{removed}}}{W_{\text{input}}} = \frac{\text{BTU/h refrigerating effect}}{3{,}412 \times \text{kW input}} $

Ton of refrigeration history: the heat required to melt 1 short ton (2,000 lb) of ice in 24 hours — equivalent to 12,000 BTU/h, agreed upon as the standard in the 1890s US ice-trade era

Device / System	Typical Power	In kW	In hp
LED light bulb	9–15 W	0.009–0.015	0.012–0.020
Laptop computer	30–65 W	0.030–0.065	0.040–0.087
Electric kettle	1,800–3,000 W	1.8–3.0	2.4–4.0
Home HVAC (1 ton)	~1,000–1,500 W input	1.0–1.5	1.34–2.01
Economy car engine	75–120 kW	75–120	100–161
Performance EV motor	300–500 kW	300–500	402–670
Boeing 787 engine (1 of 2)	~76,000 kW at takeoff	76,000	~101,900
Large coal power station	1,000–3,000 MW	1,000,000–3,000,000	1.34–4.0 M hp
US total electricity generation	~430 GW avg.	430,000,000	576 M hp

🌿 Energy efficiency insight: Power (watts) × time (hours) = Energy (watt-hours). A 10 W LED left on 24 hours consumes 240 Wh = 0.24 kWh. At a typical US electricity rate of $0.13/kWh, that costs $0.031/day — only $11.38/year. Compare to a 60 W incandescent: $68.25/year for the same light output. This 6× efficiency difference is why LED adoption saves ~150 TWh/year in the US alone.

📡 dBm to Watts — Telecommunications & RF Power

In RF (Radio Frequency) engineering and telecommunications, power is measured on a logarithmic scale using dBm (decibels relative to 1 milliwatt). This is because signal power varies over many orders of magnitude — a mobile phone transmitter may output 250 mW (+24 dBm) while a received signal at the antenna might be 0.000001 mW (−60 dBm). A linear scale would be unworkable; a logarithmic scale makes both manageable on the same chart.

dBm ↔ Watts Conversion

\[ P_{\text{dBm}} = 10 \log_{10}\!\left(\frac{P_{\text{mW}}}{1\,\text{mW}}\right) \qquad P_{\text{mW}} = 10^{P_{\text{dBm}}/10} \]

0 dBm = 1 mW · 10 dBm = 10 mW · 20 dBm = 100 mW · 30 dBm = 1,000 mW = 1 W · 40 dBm = 10 W · Every +10 dBm = ×10 power; every +3 dBm ≈ ×2 power

📶 Practical RF power reference: Typical Wi-Fi router transmit power: +20 dBm (100 mW). Mobile phone max EIRP: +23 dBm (200 mW). Broadcast FM radio station: +50 dBm (100 W). Digital TV broadcast: +60 dBm (1,000 W = 1 kW). Long-range radar: +90 dBm (1,000 kW = 1 MW).

Written & Reviewed by Num8ers Editorial Team — Electrical Engineering, Mechanical Power & HVAC Specialists Last updated: April 2026 · Conversion factors verified against NIST SP 811 (2008), BIPM SI Brochure 9th ed. (2019), SAE International standards, ASHRAE Fundamentals Handbook, and IEEE definitions of electrical power quantities.

❓ Frequently Asked Questions — Power Conversion

How do I convert horsepower (hp) to kilowatts (kW)?

Multiply by 0.745699. $1\,\text{hp} = 745.699\,\text{W} = 0.745699\,\text{kW}$. Example: 200 hp × 0.745699 = 149.1 kW. Reverse: $1\,\text{kW} = 1.34102\,\text{hp}$. Note: European metric hp (PS) is slightly different — 1 PS = 735.499 W = 0.735 kW.

How do I convert kilowatts (kW) to horsepower (hp)?

Multiply by 1.34102. $1\,\text{kW} = 1.34102\,\text{hp}$ (mechanical). Example: 150 kW × 1.34102 = 201.15 hp. A Tesla Model 3 Standard Range at 208 kW = 278.9 hp. The multiplier 1.34 is the most commonly used approximation for quick mental math.

How do I convert watts to kilowatts?

Divide by 1,000 (or move decimal 3 places left). $1\,\text{W} = 0.001\,\text{kW}$. Examples: 1,500 W kettle = 1.5 kW. 60 W bulb = 0.06 kW. 2,500 W oven = 2.5 kW. Reverse (kW to W): multiply by 1,000. Energy = power × time: 2 kW × 5 hours = 10 kWh.

How do I convert kilowatts to BTU/hour?

Multiply by 3,412.14. $1\,\text{kW} = 3{,}412.14\,\text{BTU/h}$. Example: 5 kW electric heater = 17,061 BTU/h. Reverse: $1\,\text{BTU/h} = 0.29307\,\text{W}$. Example: 12,000 BTU/h air conditioner = 3,517 W = 3.517 kW. BTU/h is the dominant unit in US residential HVAC specification.

What is a ton of refrigeration and how does it convert to kW?

1 ton of refrigeration = 12,000 BTU/h = 3.516853 kW. It originated from the heat required to melt 2,000 lb (1 short ton) of ice in 24 hours. A 5-ton HVAC system = 60,000 BTU/h = 17.58 kW of cooling capacity. Reverse: $1\,\text{kW} = 0.284345\,\text{TR}$. Note: this is the cooling capacity (heat removed), not the electrical input power.

What is the difference between kW and kVA?

kW = real (active) power; kVA = apparent power. $\text{kW} = \text{kVA} \times \text{Power Factor}$. For resistive loads (heaters, incandescent bulbs): PF = 1.0, so kW = kVA. For inductive loads (motors, transformers): PF = 0.7–0.9, so kVA > kW. A 100 kVA generator with PF 0.8 delivers only 80 kW of usable work. Generator and transformer ratings are always in kVA.

How do I convert kVA to kW?

Multiply kVA by the power factor (PF). $\text{kW} = \text{kVA} \times \cos\phi$. Example: 150 kVA at PF 0.85 = 127.5 kW. If you do not know the PF, check the equipment nameplate or datasheet. For UPS systems: PF is often 0.8–0.9. For large industrial motors: 0.85–0.95 at full load.

What is the difference between mechanical horsepower and metric horsepower (PS)?

Mechanical hp (SAE): 745.699 W — used in US automotive. Metric hp (PS/CV/ch/pk, DIN): 735.499 W — used in European/Japanese automotive. Difference: 1.35%. Example: A car rated 200 PS (European) = 197.2 mechanical hp (US equivalent). This is why European and US horsepower figures for the same car differ slightly on spec sheets.

How do I calculate power from torque and RPM?

$P\,[\text{W}] = \dfrac{2\pi \times N\,[\text{RPM}] \times T\,[\text{N·m}]}{60}$. For horsepower: $\text{hp} = \dfrac{T\,[\text{ft·lbf}] \times N\,[\text{RPM}]}{5{,}252}$. Example: 400 N·m torque at 5,000 RPM = $\frac{2\pi \times 5000 \times 400}{60} = 209{,}440\,\text{W} = 209.4\,\text{kW} = 280.8\,\text{hp}$. On a torque/power curve, they always cross at 5,252 RPM in the ft-lbf/hp system.

What is 0 dBm in watts?

0 dBm = 1 milliwatt (1 mW = 0.001 W). Formula: $P_{\text{mW}} = 10^{P_{\text{dBm}}/10}$. Key values: −30 dBm = 1 µW, −10 dBm = 100 µW, 0 dBm = 1 mW, 10 dBm = 10 mW, 20 dBm = 100 mW, 30 dBm = 1 W, 40 dBm = 10 W. Every 10 dBm increase = 10× power; every 3 dBm increase ≈ 2× power.

How much horsepower does a typical car have?

Economy cars: 75–120 kW (100–160 hp). Family sedans: 110–180 kW (150–240 hp). Performance cars: 220–370 kW (300–500 hp). Supercars: 450–750+ kW (600–1,000+ hp). Note that torque determines acceleration feel at low speed, while horsepower (= torque × RPM) determines top-speed performance. A diesel truck engine may produce 1,500 N·m torque but only 265 kW (355 hp) because it operates at low RPM.

How accurate is the Num8ers Power Conversion Calculator?

Uses exact or high-precision conversion factors per NIST SP 811 and BIPM: 1 mechanical hp = 550 ft·lbf/s = 745.69987−W (from exact 1959 foot/pound definitions); 1 BTU (IT) = 1,055.05585 J (NIST); 1 TR = 12,000 BTU/h (exact); 1 PS = 75 × 9.80665 = 735.49875 W. JavaScript double precision provides ~15 significant digits. All results are exact mathematical conversions — always verify power factor for kVA↔kW conversions in real electrical systems.

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