How Air Temperature and Radiant Temperature Differ

Why this matters

There are at least two temperatures in every room and a thermostat reports one of them. The air is one. The surfaces the occupant can see are the other, and a body exchanges heat with those surfaces directly, in straight lines, whatever the air is doing in between. That is why a room can hold 72 degrees F all day and still generate a complaint that is neither imagined nor a fault, and why the same 72 degrees F can be comfortable in the morning and unbearable at four in the afternoon with nothing about the equipment having changed.

Before you take surface readings in an occupied space

Ceiling and high-wall surfaces mean working at height. Use a non-contact instrument from the floor or a telescoping pole rather than climbing, and where you must climb, use a rated ladder on level footing, not a chair or a desk; ladder duties sit at 29 CFR 1910.23 in general industry and 29 CFR 1926 Subpart X where the work falls under construction.

Do not put a contact probe on a lighting fixture housing or a recessed can; those run hot enough to burn and getting inside one means an enclosure with live parts, which is energized electrical work under 29 CFR 1910.333(b)(2). Read the ceiling surface beside the fixture instead, which is what you wanted anyway.

If the answer sends you into the attic above, treat that as a heat stress hazard on its own terms: set a work and rest schedule before you go up, carry water, tell someone, and come out on the schedule rather than on how you feel.

Two temperatures, one thermostat

Air temperature, or dry-bulb, is what a shielded sensor in the airstream reports. It drives convective exchange: the body loses or gains heat to air moving over the skin, at a rate that goes up sharply with air speed.

Mean radiant temperature, MRT, is a single number standing in for all the surfaces an occupant exchanges radiant heat with: walls, ceiling, floor, glass, equipment. It drives radiant exchange, which is line-of-sight and set by surface temperatures rather than by air.

What a person feels is a blend. Operative temperature is the standard's name for that blend, and at low air speed it is close to the simple average of air temperature and MRT. The equal-weight version holds while air movement is low, on the order of 40 ft per minute or less; above that the air term carries more weight. ASHRAE Standard 55 defines operative temperature and the weighting, and read the current edition for the exact treatment rather than carrying a factor between jobs.

So: operative is roughly (air + MRT) / 2 in a still room. A thermostat measures the first term and reports it as though it were the answer.

Building MRT from surfaces you can actually measure

You do not need a laboratory instrument. Take the surface temperature of each significant surface the occupant can see, estimate its area, and take the area-weighted average.

Two honest limits on that method, stated up front because they change how far you can push it. True MRT weights each surface by its view factor from the occupant's position, not by its bare area, so area-weighting is an approximation that is reasonable when the occupant is somewhere near the middle of the space and gets steadily worse the closer they stand to one large surface. And a small surface at an extreme temperature moves MRT less than it moves comfort, because a cold window also produces a downdraft and a strong local asymmetry that the single averaged number does not carry. ASHRAE Standard 55 treats radiant asymmetry as its own discomfort factor with limits separate from operative temperature, and those limits differ depending on whether the offending surface is a warm ceiling, a cool wall, a cool ceiling or a warm wall.

The gate

At an occupied position, compute the area-weighted MRT of the surfaces in view. If MRT differs from air temperature by more than about 2 degrees F, the air reading alone will not predict what that occupant reports, and the productive fix is on a surface.

Unit of analysis is one occupied position, not the room. Two chairs in the same room can land on opposite sides of this gate. It is a single gate: do not additionally require that a complaint already exists, because the point of computing it is to predict where one will come from.

When it triggers, the step size follows directly from the weighting. Changing one surface's temperature moves MRT by that surface's area share multiplied by the change, and moves operative temperature by half of that at low air speed. That relationship is how you size a surface fix before you sell it.

Run the same gate against the two cases below. They resolve in opposite directions and call for opposite work.

Case A: cold surfaces, and an occupant colder than the number

A remodeled bathroom, 8 ft by 10 ft, 8 ft ceiling. Air holds 72 degrees F. The customer says it is cold.

Surfaces and areas: floor 80 sq ft of tile at 62 degrees F; one exterior wall 80 sq ft at 66 degrees F; the remaining walls 208 sq ft at 71 degrees F; ceiling 80 sq ft at 71 degrees F. Total 448 sq ft.

MRT = (80 x 62 + 80 x 66 + 208 x 71 + 80 x 71) / 448 = (4,960 + 5,280 + 14,768 + 5,680) / 448 = 30,688 / 448 = 68.5 degrees F.

Gate: 68.5 against 72 is 3.5 degrees F apart, above the 2 degree F threshold, so it triggers.

Operative = (72 + 68.5) / 2 = 70.3 degrees F. The occupant is experiencing something close to 70.3 in a room the thermostat calls 72.

Now size a surface fix using the step rule. Warming the tile floor to a 78 degrees F surface changes MRT by the floor's area share times the change: (80 / 448) x (78 - 62) = 0.179 x 16 = 2.9 degrees F. New MRT is 68.5 + 2.9 = 71.4, and operative becomes (72 + 71.4) / 2 = 71.7, up 1.4 degrees F from 70.3.

And there is a third route in this room that neither number captures: bare feet on tile is conduction, direct contact, and tile pulls heat out of skin far faster than carpet at the identical 62 degrees F would. That is why warming this particular floor delivers more comfort than its 1.4 degree F operative contribution predicts, and it is worth telling the customer that the arithmetic understates this one.

The alternative fix, raising the air setpoint, has to do all the work through one term of the average. To reach the same 71.7 operative through air alone: air = 2 x 71.7 - 68.5 = 74.9 degrees F, so almost 3 degrees F above the current setpoint, applied to the whole zone, to fix one room.

Case B: the same gate, hot surfaces, the opposite call

An upper-floor room under a roof. Air holds 78 degrees F all day. The customer says it is fine in the morning and unbearable by mid-afternoon. Two sets of surface readings, same room, same air temperature.

Surfaces and areas: ceiling 180 sq ft, walls 400 sq ft, floor 180 sq ft. Total 760 sq ft.

Morning: ceiling 78, walls 78, floor 76 degrees F. MRT = (180 x 78 + 400 x 78 + 180 x 76) / 760 = (14,040 + 31,200 + 13,680) / 760 = 58,920 / 760 = 77.5 degrees F. Gate: 77.5 against 78 is 0.5 degrees F apart. It does not trigger. Operative = (78 + 77.5) / 2 = 77.8 degrees F.

Mid-afternoon: ceiling 96, walls 80, floor 76 degrees F. MRT = (180 x 96 + 400 x 80 + 180 x 76) / 760 = (17,280 + 32,000 + 13,680) / 760 = 62,960 / 760 = 82.8 degrees F. Gate: 82.8 against 78 is 4.8 degrees F apart, so it triggers. Operative = (78 + 82.8) / 2 = 80.4 degrees F.

The air temperature was 78 degrees F at both readings. Operative moved from 77.8 to 80.4, a 2.6 degree F swing, entirely from the ceiling surface. Both figures were computed the same way from the same three surface groups, so they compare directly. The customer's report that the room changed through the day is literally accurate, and the thermostat log that says nothing changed is also literally accurate.

Size the surface fix with the step rule. Ceiling area share is 180 / 760 = 0.237. To bring MRT down to 80.0, which puts it 2.0 degrees F from air and just inside the gate, you need a 2.8 degree F drop in MRT, so the ceiling surface has to come down by 2.8 / 0.237 = 12 degrees F, from 96 to 84. Check it: (180 x 84 + 400 x 80 + 180 x 76) / 760 = 60,800 / 760 = 80.0, so the step rule lands exactly where it said it would.

Twelve degrees off a ceiling surface on a hot afternoon comes from insulation depth, an air barrier, attic ventilation or a radiant barrier above it. It does not come from more supply air into the room.

For comparison, doing it through air alone: to get operative to 78 while MRT sits at 82.8, air = 2 x 78 - 82.8 = 73.2 degrees F. That means holding this room almost 5 degrees F colder than the rest of the house, running the equipment harder, to compensate for a ceiling.

Same gate, same arithmetic, opposite sign, opposite trade doing the work.

Where the equal-weight average stops holding

The 50/50 blend is a still-air approximation, and three things break it.

Air movement. Above roughly 40 ft per minute the air term weights more heavily and the occupant also gets a direct cooling effect from the movement itself. A ceiling fan does not change either temperature; it changes what the blend is worth to a person, and only while they are in it.

Humidity. Neither term carries latent effects. A space can land on a comfortable operative temperature and still be reported as clammy, and no amount of surface work fixes that.

Clothing and activity. The same operative temperature reads differently to someone seated in light clothing and someone working. This is not a fudge factor; it is why a comfort standard specifies both.

None of those invalidate the gate. They mean the gate identifies whether surfaces are in play, which is a different question from whether the occupant will be comfortable once they are fixed.

Confirming it at the position, not at the wall

Verification here is a discipline about location, not about instruments.

Take the surface set again from the occupant's actual position, at the time of day the complaint happens, with the equipment in the same state. A morning surface survey on a case B room proves nothing about a case B room.

Then run one independent check on the blend. A dark globe of known size with a temperature sensor at its center settles at a value between air and MRT and gives you a measured operative-like reading to compare against your computed one; the improvised shop version, a dark-painted sphere or thin-walled vessel with a probe inside, given twenty minutes to settle, is directionally useful for confirming that computed MRT is on the right side of air temperature and by roughly the right amount. Where the globe and your computed figure disagree by more than a degree or two, the usual cause is that area-weighting misrepresented a surface the occupant is much closer to than the average, which is the approximation this method warned about at the top.

References

• ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy, for operative temperature, its air-speed weighting, and radiant asymmetry limits
• ASHRAE Handbook - Fundamentals, thermal comfort chapter, for mean radiant temperature and globe temperature measurement
• 29 CFR 1910.23 and 29 CFR 1926 Subpart X for ladder use; 29 CFR 1910.333(b)(2) for energized electrical work
• See related: How Radiant Heat Behaves Differently; The Space That Felt Cold at the Right Temperature