Heat Flux Converter — W/m², BTU/h·ft², langley, cal/s·cm²

The heat flux converter above translates a heat flux density between the SI watt per square metre and the units that dominate building physics, solar engineering and American HVAC practice. Type a number, choose two units, and the answer appears live, with the same quantity shown at once in W/m², BTU per hour per square foot, thermochemical calories per second per square centimetre, and langleys per minute.

Arb Digital publishes this as part of a free engineering converter library. Heat flux is where two unit families collide most awkwardly: metric thermal work runs on watts per square metre, American practice runs on BTU per hour per square foot, and meteorology and solar research still use the langley. The conversion factors between them are not round numbers, and worse, several of them depend on which definition of the calorie or the BTU the source intended.

What This Heat Flux Converter Does

Heat flux density is the rate at which thermal energy passes through a unit area. It is power per area, so its SI unit is the watt per square metre. A value of 1,000 W/m² means one kilowatt of thermal power crossing every square metre of surface, which is roughly what full midday sun delivers at sea level.

The quantity turns up everywhere heat moves across a boundary: through a wall, into a heat sink, off a furnace lining, onto a solar panel, or out of a reactor vessel. It is distinct from total heat rate, which is measured in watts and depends on how much area you are talking about, and distinct again from thermal conductivity, which describes a material rather than a flow.

This converter handles both the metric and imperial families plus the calorie-based and langley units, and it applies exact defined factors rather than the rounded values that circulate on the internet. The four-unit grid always displays the same flux in the four most widely quoted forms so you can carry a figure straight into a report without a second conversion.

The Calorie Problem: Thermochemical vs International Table

There is no single calorie. Two definitions are in wide use and they differ by about a tenth of a percent, which is small enough to be invisible in a quick check and large enough to matter in a heat balance. The thermochemical calorie is defined as exactly 4.184 joules. The International Table calorie, usually written cal_IT, is defined as exactly 4.1868 joules. Both figures are exact by definition, not measured, and both are listed in NIST Special Publication 811.

This tool uses the thermochemical calorie of 4.184 J for its calorie and langley units, and offers the International Table calorie as a separate, explicitly labelled entry. Stating this is not pedantry. A source that quotes calories per second per square centimetre without saying which calorie leaves the reader with a 0.067 percent ambiguity, and in a paper comparing measured against modelled fluxes that can be larger than the effect being studied.

The BTU has the same problem. The International Table BTU equals exactly 1,055.05585262 J and is the one used in almost all modern engineering and HVAC work, so it is what this converter uses for its BTU units. The thermochemical BTU is slightly smaller at about 1,054.35 J. Where a source simply says "BTU", the International Table definition is the safe assumption for anything published in the last several decades.

How to Use It

1. Enter your heat flux value from a datasheet, simulation output or measurement.
2. Choose the source unit, checking the reference table if your source did not specify which calorie or BTU it used.
3. Choose the target unit for your calculation or report.
4. Read the result, which updates on every keystroke. The Convert button stays available for keyboard and screen-reader users.
5. Use Swap units to reverse the conversion instantly.

The Formula: How Heat Flux Conversion Is Calculated

Everything pivots through the watt per square metre:

result = value × factor(from) ÷ factor(to)

The BTU/(h·ft²) factor is worth deriving because it is the one people most often get from an unreliable source. One International Table BTU is 1,055.05585262 J. One hour is 3,600 s. One square foot is 0.09290304 m² exactly, since the international foot is defined as exactly 0.3048 m. So the factor is 1,055.05585262 ÷ (3,600 × 0.09290304) = 3.15459075 W/m². That derivation uses only exact defined quantities from the SI system and NIST SP 811, so the result is exact to the digits shown.

The langley is defined as one thermochemical calorie per square centimetre, which is 4.184 J over 10⁻⁴ m², or 41,840 J/m². That is an energy per area, not a flux, so it becomes a flux only when divided by a time. A langley per minute is therefore 41,840 ÷ 60 = 697.3333 W/m², and a langley per day is 41,840 ÷ 86,400 = 0.4842593 W/m². Solar radiation records from the mid-twentieth century are frequently in langleys per day, which is why the unit survives in climatology long after disappearing from engineering.

Reference Table: Every Supported Unit

Each factor is the number of watts per square metre in one of that unit.

• watt per square metre (W/m²) — 1 (SI base for this quantity)
• kilowatt per square metre (kW/m²) — 1,000 W/m²
• watt per square centimetre (W/cm²) — 10,000 W/m²
• watt per square foot (W/ft²) — 10.7639104 W/m²
• BTU (IT) per hour per square foot — 3.15459075 W/m²
• BTU (IT) per second per square foot — 11,356.5267 W/m²
• calorie (thermochemical) per second per square centimetre — 41,840 W/m²
• calorie (IT) per second per square centimetre — 41,868 W/m²
• kilocalorie (th) per hour per square metre — 1.16222222 W/m²
• langley per minute — 697.333333 W/m²
• langley per day — 0.484259259 W/m²

Heat Flux Is Not Thermal Conductivity or U-Value

Three related quantities get muddled constantly. Heat flux, in W/m², is an actual rate of energy flow through an area — it depends on the temperature difference driving it. Thermal conductivity, in W/(m·K), is a property of a material describing how readily it conducts, independent of any particular situation. A U-value, in W/(m²·K), describes a whole assembly's heat transfer per unit area per degree of temperature difference.

The relationship is straightforward: heat flux equals the U-value multiplied by the temperature difference. A wall with a U-value of 0.3 W/(m²·K) across a 20-degree difference carries a heat flux of 6 W/m². You cannot convert a U-value to a heat flux without the temperature difference, and this converter deliberately excludes conductivity and U-value units so that no such cross-quantity conversion is possible from its list. For material conductivity figures, use our thermal conductivity converter; for the heat capacity side of a transient calculation, the specific heat converter.

Where Heat Flux Values Actually Land

A sense of scale catches errors that arithmetic will not. Solar irradiance at the top of the atmosphere averages around 1,361 W/m², and at sea level under clear midday sun roughly 1,000 W/m². A comfortable building envelope in winter might pass 5 to 20 W/m². The surface of a domestic radiator runs in the hundreds. A CPU heat spreader can exceed 100 W/cm², which is a million watts per square metre — three orders of magnitude above the sun.

That last figure explains why processor cooling is difficult in a way that building insulation is not. The total power is modest, but concentrating it into a small die area produces a flux density comparable to a rocket nozzle throat. When a converted value lands far outside the range you expect for its application, the usual cause is a missing factor of a hundred or ten thousand from a square-centimetre to square-metre step, since area conversions square the length factor. Our area converter is useful for checking that step in isolation.

Time Base Matters as Much as Area

Half the units on this page carry a time in their denominator, and mixing time bases is the second most common error after area. A BTU per hour per square foot and a BTU per second per square foot differ by a factor of 3,600. A langley per day and a langley per minute differ by 1,440. These are not subtle discrepancies, yet they slip through because the unit strings look similar at a glance and the numbers alone often remain plausible in a spreadsheet column.

The defence is to read the full unit string every time rather than the leading token. If a source gives you a figure labelled only "langleys", it is an energy per area, not a flux at all, and you need to know the accumulation period before it can enter this converter. Historical solar records almost always mean langleys per day when they omit the period, but almost always is not a basis for a calculation — check the metadata. Once you have a proper flux, the power converter handles the watt side and the time converter the period.

Common Mistakes to Avoid

• Not knowing which calorie a source used — thermochemical (4.184 J) and IT (4.1868 J) differ by about 0.07 percent.
• Mixing time bases — BTU per hour and BTU per second per square foot differ by a factor of 3,600.
• Confusing heat flux with U-value — flux needs a temperature difference; U-value is per degree.
• Forgetting that area conversions square — a square centimetre is one ten-thousandth of a square metre, not one hundredth.
• Treating a bare langley figure as a flux — it is an energy per area and needs an accumulation period attached.

Related Free Tools From Arb Digital

Use the thermal conductivity converter for material properties in W/(m·K), the specific heat converter for heat capacity, and the power converter for total heat rates in watts. The area converter handles the square-metre and square-foot step, the energy converter covers joules, BTUs and kilowatt-hours, and the temperature converter deals with the driving temperature difference. Everything else is in the free online tools hub.

Frequently Asked Questions