Much of the arithmetic on HVAC exams comes down to a small set of conversions and two heat formulas, and the questions are often lost on units: a kilowatt fed into a Btu formula, a temperature rise applied to the wrong airflow, a "ton" treated as a weight. This guide gives you those constants with their sources, the formulas with their assumptions, and original worked problems that show the unit check at every line. Your exam's content outline says what else it covers; this guide is about getting these particular calculations right.
The constants you must not get wrong
| Conversion | Value | Exam rounding | Where it comes from |
|---|---|---|---|
| 1 ton of cooling | 12,000 Btu/h | 12,000 | Definition (the heat to melt one ton of ice in 24 hours) |
| 1 kilowatt | 3,412.1 Btu/h (derived: 1,000 / 0.2930711) | 3,412 (some texts use 3,413) | NIST SP 811, Appendix B.8: 1 Btu (IT)/h = 0.2930711 W |
| 1 horsepower (electrical equivalent) | 746 W | 746 | Standard definition; use the value the question gives if it differs |
| Watts, single-phase | V x A (resistive loads) | as given | Ohm's law power relation |
The two heat formulas
Sensible heat in air: Q (Btu/h) = 1.08 x CFM x delta T. The 1.08 combines the density and specific heat of standard air with the 60 minutes in an hour; a manufacturer's field reference (Belimo) describes it as a standard value for typical indoor air. It does not hold at altitude or for unusual air conditions; if a question gives a different constant or an air density, use what the question gives.
Heat in water: Q (Btu/h) = 500 x GPM x delta T. The 500 combines the weight of a gallon of water, its specific heat, and the 60 minutes in an hour, for plain water in ordinary hydronic conditions (the same reference gives it for plain water); glycol mixtures use a different factor.
Both formulas can be turned around: CFM = Q / (1.08 x delta T) and delta T = Q / (1.08 x CFM). Write the version you need before you put numbers in.
Original worked problems
These are original practice examples written for this guide, not official exam questions. Every efficiency, temperature, and constant is stated in the problem. If an exam question leaves one out, that is a signal to look for it in the stem, the question's reference table, or a stated assumption, not to supply one from memory.
Problem 1: tons to Btu/h
A condensing unit is rated at 3 tons. What is its nominal cooling capacity in Btu/h?
3 tons x 12,000 Btu/h per ton = 36,000 Btu/h. Unit check: tons x (Btu/h per ton) = Btu/h.
Problem 2: electric heat strip to Btu/h
An air handler has a 10 kW electric heat strip. What heat output does it produce, ignoring fan heat?
10 kW x 3,412 Btu/h per kW = 34,120 Btu/h. Unit check: kW x (Btu/h per kW) = Btu/h. If a choice reads 3,412 Btu/h, that is the answer for 1 kW, a prefix slip.
Problem 3: furnace airflow from temperature rise
A gas furnace has an input of 80,000 Btu/h. The question states its steady-state efficiency as 80 percent and gives a measured temperature rise of 50 F across the heat exchanger. What airflow, in CFM, is the furnace moving?
Step 1: output = 80,000 x 0.80 = 64,000 Btu/h. (Use output, not input; the heat that goes up the flue does not warm the air.) Step 2: CFM = Q / (1.08 x delta T) = 64,000 / (1.08 x 50) = 64,000 / 54 = 1,185 CFM (1,185.2 before rounding). Unit check: (Btu/h) / ((Btu/h per CFM per F) x F) = CFM. Plausibility: a furnace of this size moving roughly 1,000 to 1,400 CFM is reasonable; if you had used the input, you would get 1,481 CFM, which is the most common wrong choice.
Problem 4: sensible heat from airflow and rise
An air handler delivers 1,200 CFM with a 20 F temperature difference across the coil. How much sensible heat is being moved?
Q = 1.08 x 1,200 x 20 = 25,920 Btu/h, which is about 2.16 tons of sensible capacity (25,920 / 12,000). Note that this is sensible heat only; total capacity would also include latent heat, which this formula does not capture.
Problem 5: hydronic heat
A boiler loop circulates 5 GPM with a 20 F drop across a coil. What is the heat delivered?
Q = 500 x 5 x 20 = 50,000 Btu/h. Unit check: (Btu/h per GPM per F) x GPM x F = Btu/h.
Problem 6: from electrical nameplate to Btu/h
A 240-volt, single-phase electric heater draws 20 amperes. What is its heat output in Btu/h?
Step 1: watts = 240 x 20 = 4,800 W = 4.8 kW. Step 2: 4.8 x 3,412 = 16,378 Btu/h (16,377.6 before rounding). The two traps are using 4,800 as kilowatts (answer off by 1,000) and forgetting to convert watts to kilowatts at all.
Problem 7: temperature rise check
A furnace nameplate lists an allowable temperature rise range of 40 to 70 F (as given in the question). The measured supply air is 128 F and the return air is 68 F. Is the rise within range, and what does it suggest?
Rise = 128 minus 68 = 60 F. It is within the stated 40 to 70 F range. If it had been above the top of the range, the usual interpretation in training materials is low airflow (dirty filter, closed registers, undersized blower); below the range suggests high airflow or low output. The question's stated range governs; do not substitute a range from memory.
A unit check you can run in ten seconds
- Write the unit the question wants (Btu/h, CFM, F, tons).
- Write the units of every number you are about to multiply or divide.
- Cancel. If the leftover unit is not the one from line 1, stop and fix the setup.
- Only then press the calculator keys.
This is the same discipline the electrical calculation checking routine teaches; the formulas differ, the habit is identical.
Common errors, listed
- Using furnace input where output is needed (Problem 3).
- Applying 1.08 to a problem that supplied a different constant for altitude.
- Treating a "ton" as 2,000 pounds of anything.
- Mixing kW and W (Problems 2 and 6).
- Reporting sensible heat as total capacity (Problem 4).
- Subtracting supply from return and reporting a negative rise.
Practice next
Take the free HVAC practice test with a calculator and run the ten-second unit check on every numeric question. The Heating Systems topic and the Refrigeration and Air Conditioning topic cover the equipment behind Problems 3, 4, and 7, and the HVAC study guide places the math week in the full sequence.
Sources and verification notes
The kilowatt-to-Btu/h conversion is derived from the NIST SP 811 factor 1 Btu (IT)/h = 0.2930711 W. The 1.08 sensible-heat formula, the 500 hydronic formula, and 12,000 Btu/h per ton are taken from a manufacturer field reference (Belimo); the 1.08 constant assumes standard air and the 500 constant plain water. The 746 W per horsepower figure is the customary electrical equivalent. Efficiencies, temperature-rise ranges, and airflow figures in the problems are stated in the problems and are original practice examples, not equipment data or official exam questions. Whether a given exam supplies constants is not something this guide can promise; read the stem.
- NIST Special Publication 811, Appendix B.8 (unit conversion factors)Checked September 18, 2026
- Belimo, HVAC Formulas and Calculations Field Reference Guide (1.08 and 500 formulas, 12,000 Btu/h per ton)Checked September 18, 2026
Written by the ExamsLib editorial team. Practice examples in this guide are original and are not official exam questions. Exam rules change; the candidate bulletin from your licensing authority is the final word. Found an error? Contact us.
