Convert Energy Units
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📘 Overview
“Energy” shows up as electricity (kWh), heat (BTU), nutrition (Cal), mechanical work (ft·lbf), and particle physics (eV). Conversions are straightforward when the unit definition is clear, and misleading when a unit has multiple conventions.
For related tools and context pages, see Unit Converters, Energy, Home & DIY, Cooking.
What the main units represent
- Joule (J): SI energy. 1 J = 1 N·m = 1 W·s.
- Kilowatt-hour (kWh): utility billing energy (power × time).
- BTU: heat-energy unit used in HVAC and fuel/heat reporting.
- Cal (nutrition): commonly used for food energy (often written “Calories”).
- Electronvolt (eV): atomic/particle scale energy.
- toe / TCE: standardized “fuel-equivalent” energies for statistics and reporting.
Quick reality-check table (spot the 10× / 1000× errors)
| Anchor value | Approx. equivalents | Typical place you see it | Common mistake |
|---|---|---|---|
| 1 kWh | 3.6×106 J | Electricity bills | Confusing Wh with kWh (1000×) |
| 1 BTU | ≈1055 J | HVAC sizing, heat content | Mixing BTU definitions (small % drift) |
| 1 Cal (food) | ≈4184 J | Nutrition labels | Mixing “cal” vs “Cal” (1000×) |
| 1 ft·lbf | ≈1.356 J | Mechanical work/torque contexts | Using in·lbf as if it were ft·lbf (12×) |
| 1 eV | ≈1.6×10-19 J | Atomic physics | Rounding to zero instead of using scientific notation |
Edge case note: negative values can represent an energy change (ΔE) in calculations, even though many “energy amounts” are non-negative by definition. Interpret the sign according to your context.
📐 Formula & Methodology
Reliable conversion is a scale transform. The safest approach is converting everything through the SI pivot unit: joules (J). This avoids chaining factors across unrelated unit families.
E(J) = value × factor(from → J) value(to) = E(J) ÷ factor(to → J)
Definition-aware notes (where energy units differ)
- kWh is exact: 1 kWh = 1000 W × 3600 s = 3.6×106 J.
- BTU varies by standard: many references use IT vs thermochemical BTU; expect small differences across tables.
- Calories are overloaded: “Cal” (food) usually means kilocalorie; “cal” (small calorie) is 1/1000 of that.
- Fuel-equivalent units: toe/TCE/“ft³ natural gas” are statistical conventions; they may be based on HHV vs LHV or regional assumptions.
- p×V units: “L·atm”, “scf”, “scc” represent pressure–volume work units, not chemical energy.
Frequent conversion mistakes (math/logic, not UI)
- Wh vs kWh: forgetting that kWh is 1000× Wh is the #1 scale error in energy work.
- cal vs Cal: mixing lower-case calorie with nutrition Calorie creates a 1000× error.
- BTU per hour confusion: BTU is energy; BTU/h is power. Convert power with time explicitly.
- ft·lbf vs lbf·ft: torque and work share units; energy conversion needs “distance moved,” not just torque.
- Rounding too early: rounding intermediate J values can distort tiny units (eV/Eh/Ry) by orders of magnitude.
Reference factors snapshot (selected)
| Unit | Symbol | → J | Note |
|---|---|---|---|
| Joule | J | 1 | SI base unit |
| Kilowatt-hour | kW·h | 3.6×10⁶ | Electricity billing unit |
| Calorie | Cal | 4184 | Food-energy unit (kcal) |
| BTU | BTU | 1055.056 | Heating/cooling |
| Electronvolt | eV | 1.602×10⁻¹⁹ | Particle physics |
| Celsius heat unit | CHUIT | 4184 | Same as 1 dietary Calorie |
| Standard cm³ atm | cc atm | 101325 × 10⁻⁶ | 1 cm³ of air at STP |
| Standard ft³ atm | scf | 101325 × 0.0283168 | 1 ft³ of air at STP |
| Standard yd³ atm | scy | 101325 × 0.764555 | 1 yd³ of air at STP |
| Foot-pound force | ft·lbf | 1.3558179 | Mechanical work |
| Foot-poundal | ft·pdl | 0.04214 | CGS mechanical |
| Imp gal atm | imp gal atm | 101325 × 0.0045461 | Imperial gallon of air at STP |
| US gal atm | US gal atm | 101325 × 0.00378541 | US gallon of air at STP |
| Hartree | Eh | 4.359744e-18 | Atomic unit of energy |
| Erg | erg | 1e-7 | CGS energy |
| Horsepower-hour | hp·h | 2.685e6 | Engine work |
| In-pound force | in·lbf | 0.1129848 | Small mechanical |
| Kilocalorie | kcal | 4184 | Same as Cal |
| kW·h (BOTU) | B.O.T.U. | 3.412e6 | US Board of Trade |
| Litre-atm | l·atm | 101325 | Gas work |
| Quad | quad | 1.055e18 | US energy industry |
| Rydberg | Ry | 2.179872e-18 | Atomic physics |
| Therm (E.C.) | thermEC | 1.055e8 | European gas |
| Thermie | th | 4.1868e6 | Metric ton‐calorie |
| TCE | TCE | 2.94e10 | Tonne coal eq. |
| toe | toe | 4.1868e10 | Tonne oil eq. |
| Ton TNT | tTNT | 4.184e9 | Explosive yield |
| Watt-second | W·s | 1 | Same as Joule |
🧪 Examples
Example 1: 2.5 kWh → joules (bill-to-SI)
- 2.5 kWh × 3.6×106 = 9.0×106 J
- Sanity check: kWh should land in the “millions of joules” range.
Example 2: 500 Cal → kWh (nutrition-to-utility)
- 500 Cal × 4184 ≈ 2.092×106 J
- 2.092×106 J ÷ 3.6×106 ≈ 0.581 kWh
- Sanity check: a few hundred Calories is under 1 kWh.
Example 3: 10,000 BTU → kWh (HVAC energy)
- 10,000 BTU ≈ 10,000 × 1055 ≈ 1.055×107 J
- 1.055×107 J ÷ 3.6×106 ≈ 2.93 kWh
- Tip: don’t confuse BTU with BTU/h (power).
Example 4: 1,000,000,000 eV → joules (particle scale)
- 109 eV × 1.602×10-19 ≈ 1.602×10-10 J
- Tip: large eV counts can still be tiny in joules.
💡 Use Cases
- Electricity vs heat: compare kWh with BTU when reading HVAC specifications or energy bills.
- Nutrition context: relate Calories to kWh to build intuition about energy scales (not a diet recommendation).
- Engineering work: convert ft·lbf or hp·h into SI for reports and calculations.
- Science/education: convert eV/Eh/Ry into joules for physics and chemistry problems.
- Energy statistics: interpret toe/TCE/quad values when reading industry or national datasets.
Tips that prevent wrong conclusions
- Keep units paired with time: power (W, BTU/h) needs a duration to become energy (J, kWh, BTU).
- Delay rounding: round at the end, especially when converting to/from eV or atomic units.
- Check the definition first: if a result differs from another source, compare the BTU/calorie/therm convention before changing inputs.
For scaling and number-format help in scientific notation contexts, you can cross-check with tools in Data.
❓ Frequently Asked Questions
Why do conversions pivot through joules (J)?
Joule (J) is the SI unit of energy (1 J = 1 N·m). Converting via J reduces chained-rounding errors when jumping between unrelated unit families like kWh, BTU, and eV.
Is “Calorie (Cal)” the same as kcal?
In nutrition, Calorie (Cal) and kilocalorie (kcal) are used interchangeably. Different scientific conventions exist for the small “cal” and for the exact J-per-cal value, so match your reference when precision matters.
What’s the fastest sanity check between kWh and joules?
1 kWh = 3.6×10^6 J exactly, because 1 W = 1 J/s and 1 hour = 3600 s. If you’re off by 1000×, you likely mixed Wh and kWh.
Why can BTU conversions differ between sources?
BTU has multiple definitions (e.g., IT vs thermochemical). Many tables round aggressively, so you may see small differences in the 4th–6th significant digit.
What does “therm” mean here?
Therm is a large energy unit used in gas billing and energy reporting. There are regional definitions (e.g., U.S. therm vs other conventions), so always check what your bill or standard uses.
What are toe and TCE used for?
toe (tonne of oil equivalent) and TCE (tonne of coal equivalent) are energy accounting units used in statistics and industry reports. They represent standardized fuel-equivalent energies, not literal masses being burned.
What is a quad?
A quad is used in U.S. energy statistics and equals 10^15 BTU. It’s useful for national-scale totals, where J or kWh would be unwieldy.
Why are eV, Hartree (Eh), and Rydberg (Ry) so tiny in joules?
These are atomic-scale units, so their J equivalents are extremely small. Scientific notation is the correct way to read results without losing magnitude.
What’s the difference between ft·lbf and in·lbf?
They are the same work unit with different distance bases: 1 ft·lbf = 12 in·lbf. Confusing inch-pound force with foot-pound force creates a 12× error.
What is “horsepower-hour (hp·h)”?
hp·h is power integrated over time: (horsepower) × (hour). It’s used in legacy engine/industrial contexts; compare it to kWh to avoid scale mistakes.
Do “scf”, “scc”, and “L·atm” represent fuel energy?
Not by default. These are pressure–volume work units (p×V) expressed using “atmosphere × volume” at stated standard conditions; they are not the chemical heat content of the gas unless a specific heating-value convention is applied.
How should I handle rounding and significant figures?
Keep extra digits during conversion and round once at the end. If two sources disagree slightly, compare the underlying unit definition (IT vs thermochemical) before assuming one is wrong.
Assumptions & limits:
Energy-unit names like BTU, calorie, therm, and fuel-equivalent units can have multiple published definitions (regional standards, IT vs thermochemical, HHV vs LHV conventions).
Results are only as “standard” as the factor set used for the selected unit and should be matched to your bill/spec/standard when precision or compliance matters.
Educational disclaimer:
Conversions are provided for informational use only. No guarantees are made for regulatory, billing, engineering, safety, or contractual purposes.
Reference/attribution:
Core SI relationships follow the International System of Units (SI) definitions (e.g., J = W·s) and common published engineering conventions for legacy units.
Last review: January 2026