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Joule to Horsepower-hour (metric) Calculator & Formula (J to hp·h (metric))

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Live Conversion • ISO 80000-5:2019 Certified
1 Joule = 3.77672671 × 10⁻⁷ Horsepower (metric) hour
1 J = 3.776727 × 10⁻⁷ hp·h (metric) • 1 hp·h (metric) = 2647795.5 J
Joule to Horsepower (metric) hour: One Joule is equal to 3.77672671 × 10⁻⁷ Horsepower (metric) hours.
Certified Authority Value
0.00000038
hp·h (metric)
Exact: 1 hp·h (metric) ≡ 2647795.5000000005 J
J
J
Swap to Horsepower (metric) hour to Joule
hp·h (metric)
hp·h (metric) 3.77672671 × 10⁻⁷
Quick Values:
1 J 5 J 10 J 25 J 50 J 100 J 250 J 500 J 1,000 J
Conversion Formula
To convert Joule to Horsepower (metric) hour, multiply by 3.77672671 × 10⁻⁷
J × 3.77672671 × 10⁻⁷ = hp·h (metric)

Calculation: 1 J × 3.77672671 × 10⁻⁷ = 3.77672671 × 10⁻⁷ hp·h (metric)

Common Joule to Horsepower (metric) hour Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Joule (J) and Horsepower (metric) hour (hp·h (metric)).

Tap any row to calculate
Joule to Horsepower (metric) hour: Primary Direct Table (15 Steps)
Joule to Horsepower (metric) hour Conversion Reference Table
Conversion & Equivalent Value Scientific Notation
0.001 J is equal to 3.776727 × 10⁻¹⁰ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻¹⁰
0.01 J is equal to 3.776727 × 10⁻⁹ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁹
0.1 J is equal to 3.776727 × 10⁻⁸ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁸
0.5 J is equal to 1.888363 × 10⁻⁷ hp·h (metric) (Horsepower (metric) hour) 1.888 × 10⁻⁷
1 J is equal to 3.776727 × 10⁻⁷ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁷
2 J is equal to 7.553453 × 10⁻⁷ hp·h (metric) (Horsepower (metric) hour) 7.553 × 10⁻⁷
5 J is equal to 1.888363 × 10⁻⁶ hp·h (metric) (Horsepower (metric) hour) 1.888 × 10⁻⁶
10 J is equal to 3.776727 × 10⁻⁶ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁶
20 J is equal to 7.553453 × 10⁻⁶ hp·h (metric) (Horsepower (metric) hour) 7.553 × 10⁻⁶
25 J is equal to 9.441817 × 10⁻⁶ hp·h (metric) (Horsepower (metric) hour) 9.442 × 10⁻⁶
50 J is equal to 1.888363 × 10⁻⁵ hp·h (metric) (Horsepower (metric) hour) 1.888 × 10⁻⁵
100 J is equal to 3.776727 × 10⁻⁵ hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁵
250 J is equal to 9.441817 × 10⁻⁵ hp·h (metric) (Horsepower (metric) hour) 9.442 × 10⁻⁵
500 J is equal to 0.000188836 hp·h (metric) (Horsepower (metric) hour) 1.888 × 10⁻⁴
1000 J is equal to 0.000377673 hp·h (metric) (Horsepower (metric) hour) 3.777 × 10⁻⁴
Horsepower (metric) hour to Joule: Reciprocal Summary
Horsepower (metric) hour to Joule Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 hp·h (metric) is equal to 2647795.5 J (Joule) 2.648 × 10⁶
5 hp·h (metric) is equal to 1.323898 × 10⁷ J (Joule) 1.324 × 10⁷
10 hp·h (metric) is equal to 2.647796 × 10⁷ J (Joule) 2.648 × 10⁷
50 hp·h (metric) is equal to 1.323898 × 10⁸ J (Joule) 1.324 × 10⁸
100 hp·h (metric) is equal to 2.647796 × 10⁸ J (Joule) 2.648 × 10⁸
View Complete 15-Row Horsepower (metric) hour to Joule Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Joule (J) and Horsepower (metric) hour (hp·h (metric)):

Joule References:

  • Mechanical work required to lift a medium culinary apple vertically by one meter 1 J
  • Kinetic energy of a standard tennis ball dropped from waist height 1 J
  • Energy consumed by a 1-watt LED pilot lamp operating for one second 1 J

Horsepower (metric) hour References:

  • Mechanical work performed by one metric horsepower engine running for one hour (2.648 MJ) 1 hp·h (metric)

Tap any benchmark above to automatically calculate its exact equivalent in Horsepower (metric) hour.

ISQ Dimension: [M L² T⁻²] Coherent SI Unit: joule (J) Chemical Engineering, Solutions & Physical Chemistry

How to Convert Joule to Horsepower (metric) hour

Converting Joule (J) to Horsepower (metric) hour (hp·h (metric)) is a core calculation in Energy and Work, which quantifies the physical capacity to perform mechanical work, generate heat, or emit electromagnetic radiation. This calculation navigates the boundary between the International Metric System (SI) and British Imperial / US Customary engineering standards. In contemporary metrology, Imperial units are defined in terms of exact SI standards via international agreements—notably NIST SP 811 and the 1959 International Yard and Pound Agreement. Exactly 1 Joule equals 3.776727 × 10⁻⁷ Horsepower (metric) hour, while 1 hp·h (metric) equals 2647795.5 J.

Direct Factor1 J = 3.776727 × 10⁻⁷ hp·h (metric)
Inverse Ratio1 hp·h (metric) = 2647795.5 J
Conversion ScaleMetric SI to British Imperial / US Customary Bridge
First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (joule (J)) without arbitrary rounding:

Vtarget=Vsource×(ksource→SIktarget→SI)V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)
Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)
1. Source SI Bridge (ksource):1 J = 1 joule (J)
2. Target SI Bridge (ktarget):1 hp·h (metric) = 2647795.5 joule (J)
Step-by-step substitution for Joule → Horsepower (metric) hour:V(hp·h (metric)) = V(J) × ( 1 / 2647795.5 ) = V(J) × 3.776727 × 10⁻⁷
Mathematical FormulaValue in Horsepower (metric) hour = Value in Joule × 3.77672671 × 10⁻⁷Direct computational formula applied for standard conversion.
Worked Example

Converting 8 J yields an exact output of 3.021381 × 10⁻⁶ hp·h (metric) in Horsepower (metric) hour. Under higher industrial throughput, 10000 J translates to 0.00377673 hp·h (metric).

Inverse check: 1 hp·h (metric) = 2647795.5 J.

Understanding Joule and Horsepower (metric) hour

Joule

J
Coherent SI Unit

The joule (J) is the coherent SI-derived unit of energy, work, and heat, named after James Prescott Joule.

Applications & Practical Context

In practical energy terms, a mechanical work required to lift a medium culinary apple vertically by one meter equals 1 J, a kinetic energy of a standard tennis ball dropped from waist height equals 1 J, a energy consumed by a 1-watt LED pilot lamp operating for one second equals 1 J.

Physical Setup

An energy of 1 joule is the work done by a force of 1 newton acting through a displacement of 1 meter, or dissipating 1 watt of electrical power over 1 second.

Conversion to SI Unit: joule (J)
1 J = 1 N·m = 1 W·s

Horsepower (metric) hour

hp·h (metric)
Standard Unit

A Horsepower (metric) hour (hp·h (metric)) is a recognized unit for energy and work.

Applications & Practical Context

In practical energy terms, a mechanical work performed by one metric horsepower engine running for one hour (2.648 MJ) equals 1 hp·h (metric).

Physical Setup

An energy quantity of 1 hp·h (metric) corresponds to 2647795.5 J (performing 2647795.5 joules of work or heat transfer).

Conversion to SI Unit: joule (J)
1 hp·h (metric) = 2647795.5 J

Domain Metrology & Engineering Applications

Governing Law & Equation

First Law of Thermodynamics (Conservation of Energy: ΔU = Q - W)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using isoperibol bomb calorimeters, optical laser pulse joulemeters, and digital revenue-grade electric energy meters.

Primary Industry Sectors

Applied across electric power utility metering, thermal energy storage design, chemical plant process enthalpies, and ballistic impact engineering under international metrology standard ISO 80000-5:2019, NIST SP 811.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering ReferenceReference ValueConverted to Horsepower (metric) hour
Mechanical work required to lift a medium culinary apple vertically by one meter1 J3.776727 × 10⁻⁷ hp·h (metric)
Kinetic energy of a standard tennis ball dropped from waist height1 J3.776727 × 10⁻⁷ hp·h (metric)
Energy consumed by a 1-watt LED pilot lamp operating for one second1 J3.776727 × 10⁻⁷ hp·h (metric)
Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-5:2019, NIST SP 811 and the BIPM SI Brochure (9th Edition). Governed by First Law of Thermodynamics (Conservation of Energy: ΔU = Q - W) under ISO 80000 dimensional vector [M L² T⁻²].

Multi-Variable Engineering Bridge Grid Energy & Industrial Work

Continuous Power & Operating Duration Bridge (kWh • Megajoules • BTU • Average Power • Battery Runtime)

Bridge instantaneous work rate [M L² T⁻³] and accumulated energy consumption [M L² T⁻²] over operational shifts and duty cycles via the work-power equation E = P × t.

E = P × t
Live Calculated Bridge Equivalent:
1 J at 1-Hour Standard Benchmark Runtime = 0.001 kWh
Equals 0.0036 MJ • 3.41 BTU • 3600 J
Utility Standard
0.001
kWh
Kilowatt-Hours
SI Metric Energy
0.0036
MJ
Megajoules
HVAC & Thermal
3.41
BTU
British Thermal Units
SI Base Unit
3600
J
Joules
Grid Power Scale
1 × 10⁻⁶
MWh
Megawatt-Hours
Mechanical Work
0.001341
hp·h
Horsepower-Hours
  1. 1. Normalize Input to SI Base Unit (W):
    P = 1 J × 1 = 1 W
  2. 2. Apply Engineering Parameter (t):
    Selected condition: 1-Hour Standard Benchmark Runtime at t = 3600 Seconds / Hours
  3. 3. Execute Governing Physical Law in SI Units:
    E = P × t = (1) × (3600) = 3600 J
  4. 4. Convert to Standard Engineering Units:
    • kWh: 3600 × 2.7778 × 10⁻⁷ = 0.001 kWh (Kilowatt-Hours) • MJ: 3600 × 1 × 10⁻⁶ = 0.0036 MJ (Megajoules) • BTU: 3600 × 0.0009478 = 3.41 BTU (British Thermal Units) • J: 3600 × 1 = 3600 J (Joules) • MWh: 3600 × 2.7778 × 10⁻¹⁰ = 1 × 10⁻⁶ MWh (Megawatt-Hours) • hp·h: 3600 × 3.7251 × 10⁻⁷ = 0.001341 hp·h (Horsepower-Hours)
Explore Full Power Converter →
Engineering Substance / Operating Standard Parameter Value (Seconds / Hours) Reference State / Condition Typical Industrial & Engineering Application
1-Second Pulse (Inrush / Circuit Breaker) 1 1.0 second Motor inrush peak & capacitor discharge
1-Minute Short Cycle (Microwave / Lift) 60 60 seconds Elevator transit & commercial appliance duty
1-Hour Standard Benchmark Runtime 3600 3,600 seconds Standard utility kilowatt-hour energy basis
8-Hour Factory Shift (Industrial Machinery) 28800 8.0 hours Single industrial production line workday
24-Hour Continuous Day (Data Center / Pump) 86400 24.0 hours Always-on server racks & municipal water treatment
7-Day Continuous Week (Chemical Refining) 604800 168.0 hours Continuous manufacturing process plant run
30-Day Monthly Billing Cycle 2592000 720.0 hours Electric utility meter billing period
365-Day Annual Base Load Operation 3.1536 × 10⁷ 8,760 hours Grid generator annual capacity factor calculation
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Frequently Asked Questions

There are exactly 3.77672671 × 10⁻⁷ horsepower (metric) hours (hp·h (metric)) in 1 joule (J). To calculate larger amounts manually, simply multiply your total number of joules by the conversion multiplier of 3.77672671 × 10⁻⁷.

The mathematical formula to convert joules to horsepower (metric) hours is: [value] * 3.77672671 × 10⁻⁷ = horsepower (metric) hours. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from horsepower (metric) hours back to joules, you must divide your starting value by 3.77672671 × 10⁻⁷. Our bidirectional tool automatically computes this inverse equation the moment you type into the horsepower (metric) hour input field.

1 Horsepower (metric) hour is larger than 1 Joule. Specifically, 1 Joule equals 3.77672671 × 10⁻⁷ horsepower (metric) hours, meaning 1 Horsepower (metric) hour is 2647795.5 times larger than 1 Joule (a difference of 6.42 orders of magnitude). Expressing measurements in joules requires a larger numerical value to represent the equivalent physical magnitude.

A typical mechanical work required to lift a medium culinary apple vertically by one meter measures 1 J, which corresponds to 3.7767 × 10⁻⁷ Horsepower Metric Hour (Horsepower (metric) hour).

For mechanical energy metrology, one Joule is equal to 3.77673 × 10⁻⁷ metric Horsepower-hours. Expressed in KaTeX: 1 J = 3.77673 × 10⁻⁷ hp·h (metric).

To calculate metric Horsepower-hours from Joules, multiply the Joule magnitude by 3.77673 × 10⁻⁷. The formula is: V(hp·h (metric)) = V(J) × 3.77673 × 10⁻⁷.

To find Joules from metric Horsepower-hours, multiply the hp·h value by 2.64780 × 10⁶. The inverse function is: V(J) = V(hp·h (metric)) × 2.64780 × 10⁶.

Metric Horsepower-hours (hp·h) are historically used in European automotive and heavy machinery engineering to quantify total work output over time, though Joules and kilowatt-hours are now more prevalent under modern ISO standards.

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