Joules/second to BTU/hour

In dimensional analysis and physics derivations, writing J/s keeps the units transparent — you can see exactly what's being divided and multiplied. If you're calculating power as force × velocity (N·m/s = J/s), keeping it as J/s avoids a mental leap. Students and textbook authors prefer it when teaching the concept of power, because "energy per time" is more intuitive than a named unit. Once you understand it, you switch to watts for brevity.

The SI system officially defines the watt as the named unit for power, with J/s as its definition. In metrology documents and BIPM publications, you'll see W = J/s = kg·m²/s³. Some ISO standards for calorimetry and heat flow measurements express power in J/s to maintain consistency with energy measurements also given in joules. In practice, scientific papers in thermodynamics and physical chemistry often prefer J/s for clarity.

It makes unit cancellation visible. If you know a machine delivers 500 J of work over 10 seconds, writing 500 J ÷ 10 s = 50 J/s is a complete, self-checking calculation. Converting immediately to "50 W" obscures the path. In thermodynamics, where you track joules of heat, joules of work, and joules per second of power flow, keeping J/s prevents sign and unit errors that plague students.

J/s = W = V·A = kg·m²/s³. Each form has its domain: electrical engineers think V·A, mechanical engineers think N·m/s, and physicists think kg·m²/s³. The beauty of SI is that they're all identical. A volt is a J/C, an ampere is C/s, so V·A = J/C × C/s = J/s. This chain of definitions means you can derive any electrical quantity from mass, length, time, and current.

Never — they are exactly identical by definition, with zero rounding or conversion error. 1 J/s = 1 W, always. This is unlike, say, calories per second vs. watts, where a conversion factor (4.184) introduces potential rounding issues. The equivalence is definitional, not empirical. If someone claims a difference exists, they're confusing joules per second with some other energy-per-time unit like calories per second or BTU per hour.

The classic rule: 20 BTU/h per square foot. A 300 sq ft bedroom needs about 6,000 BTU/h; a 500 sq ft living room about 10,000 BTU/h. But this varies wildly with sun exposure (+10% for south-facing), ceiling height, insulation quality, number of occupants (+600 BTU per person), and climate zone. A room above a pizza oven in Phoenix needs more than a basement in Seattle. When in doubt, oversize slightly — an undersized unit runs constantly and never reaches setpoint.

Undersizing is obvious — the unit runs constantly and never reaches the thermostat setpoint on hot days. But oversizing is worse in subtle ways. An oversized AC cools the air quickly then shuts off before removing enough humidity, leaving you with a clammy 72°F house. The short cycles also wear the compressor faster (startup is the hardest moment) and waste energy. A 1-ton oversize in a humid climate like Florida can raise indoor humidity from a comfortable 45% to a muggy 60%. Proper Manual J load calculations matter more than most homeowners realize.

Exactly 12,000 BTU/h. One ton of AC is the cooling effect of melting one short ton (2,000 lbs) of ice over 24 hours. The ice absorbs 288,000 BTU of heat as it melts (2,000 lbs × 144 BTU/lb latent heat), divided by 24 hours = 12,000 BTU/h. Residential systems run 1.5–5 tons; commercial buildings 10–500 tons. The "ton" unit persists because HVAC contractors think in tons — "that house needs a 3-ton unit" is faster than "that house needs 10.5 kW of cooling."

Modern units achieve 12–25 BTU/h per watt of electricity (SEER 12–25). A SEER 20 unit removes 20 BTU/h of heat for every watt consumed — effectively a 3:1 heat pump ratio. That 12,000 BTU/h window unit draws 500–1,000 W of electricity depending on efficiency. The best mini-splits achieve SEER 30+, removing 30 BTU/h per watt, making them cheaper to run than resistive electric heaters even in heating mode.

A gas furnace's BTU/h rating is its thermal output after combustion efficiency losses (typically 80–96% of fuel input). A heat pump's BTU/h rating is the heat delivered including energy moved from outside — at COP 3, a heat pump delivering 36,000 BTU/h uses only 12,000 BTU/h worth of electricity. This makes direct BTU/h comparisons misleading: a 60,000 BTU/h furnace and a 60,000 BTU/h heat pump deliver the same heat, but the heat pump uses one-third the energy.