Rounding up and rounding down

A load calculation gives you 47 amperes. Do you fit a 45 A breaker or a 50 A one?

There is no general answer. It depends entirely on whether the 47 is a minimum you must meet or a maximum you must not exceed — and the two are indistinguishable from the number itself. This is, in our experience, the single most reliable source of confidently wrong answers in electrical calculation, because everything about it looks like ordinary arithmetic right up until an inspector reads the nameplate.

Floors and ceilings

Every code figure that feeds a device or conductor selection is one of two things.

A floor is the least that will do. Conductor ampacity requirements, minimum service size, the 125% continuous-load figure, a required grounding conductor. Meet it or exceed it; going bigger is permitted and usually just costs money.

A ceiling is the most you may fit. Motor branch-circuit short-circuit protection, the MOCP printed on air-conditioning equipment, the tap rules. Stay at or below it; going bigger is a violation, regardless of how safe it feels.

Round toward compliance. For a floor, that is up. For a ceiling, that is down. The arithmetic is the same; the direction is set by which kind of figure you started with.

Why the ladder makes this bite

If devices came in every size the question would barely arise. They do not. The standard overcurrent ratings in 240.6(A) run 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 110, 125 and upward, and transformer, generator and UPS sizes come in their own coarse ladders.

So a calculation almost never lands on a rung. It lands between two, and you have to move. Moving the wrong way is not a rounding error of a few percent — it is a whole device size, and on a ceiling it is a violation.

Worth noticing: the gaps are not even. Between 45 and 50 is about 11%; between 100 and 110 is 10%; between 200 and 225 is 12.5%. The practical consequence is that where your calculation falls between rungs matters as much as what it is, and a load list trimmed by a few percent sometimes drops a whole size. The transformer sizing calculator makes that visible deliberately.

Which is which

Round up — these are floors.

• Conductor ampacity for a load: take the next conductor that meets it.
• Continuous loads at 125%, for both conductor and device.
• Minimum service or feeder size from a load calculation. 47 A of computed demand does not fit a 45 A service.
• Motor branch-circuit conductors under 430.22 — 125% of table full-load current, and then up to the next conductor that carries it.
• Grounding electrode and equipment grounding conductors from their tables.
• Generator, battery bank and capacitor bank capacity.

Round down — these are ceilings.

• Motor branch-circuit short-circuit and ground-fault protection under Table 430.52. The percentage — 250% for an inverse-time breaker — is a maximum permitted, so you take the largest standard rating at or under it.
• The MOCP on air-conditioning and refrigeration equipment. The manufacturer computed it; exceeding it violates 440.4(B) and voids the listing.
• Any figure the code or a manufacturer describes as a maximum.

The same physical circuit can involve both. On a motor circuit the conductor rounds up and the device rounds down, from the same table current, in the same calculation. The motor FLA calculator runs both directions on one screen for exactly that reason.

The case that catches everyone

An air conditioner with MCA 28 A and MOCP 47 A.

The conductor is a floor: it must carry at least 28 A. At the 75 °C copper column, 12 AWG gives 25 A, which is short, so 10 AWG at 35 A. Rounded up.

The device is a ceiling: 47 A is not a standard rating, and the 240.6(A) list goes 40, 45, 50. The answer is 45 A — the largest that stays under. Rounded down.

Treat that 47 the way you would treat a general continuous load and you round up to 50 A, which is what a breaker sizing tool will tell you if you feed it 47 A without saying where the number came from. That installation exceeds the manufacturer’s stated maximum. It will be failed, and it should be.

Run it in the heat pump and HVAC calculator, which rounds down and says on the page that it is doing so.

The finished circuit — a 45 A breaker protecting 10 AWG conductors rated 35 A — looks wrong to anyone trained on general branch circuits, where the device never exceeds the conductor. In Article 440 it is correct: the branch-circuit device covers short circuits and ground faults only, and overload protection lives inside the equipment.

The next-size-up rule, and its limits

240.4(B) permits rounding a conductor’s overcurrent device up to the next standard rating when the conductor’s ampacity does not correspond to one — subject to conditions: not for receptacle-supplying branch circuits, and only up to 800 A.

It is a genuine allowance and worth knowing. It is also the rule most often stretched past its conditions, and it does not touch ceilings at all. It permits a device slightly larger than the conductor’s ampacity; it never permits a device larger than a stated maximum.

And 240.4(D), the small-conductor rule, sits on top of everything: 14 AWG copper is capped at 15 A, 12 AWG at 20 A, 10 AWG at 30 A, regardless of what the ampacity table or any derating says. A separate, absolute ceiling — which is why a correctly derated 10 AWG conductor good for 33 A still gets a 30 A breaker.

Rounding for display

One smaller point, since this site shows a lot of intermediate arithmetic.

Displayed figures are rounded for reading; calculations are not. A voltage drop shown as 3.07% was computed at full precision and rounded once, at the end. Rounding at each step accumulates error, and near a threshold that error decides the answer — which is exactly where it must not.

It is also why a result reported as just inside a limit deserves a second look rather than relief. A conductor that comes out at 2.98% against a 3% target is not comfortably inside anything.

The short version

Before you round, ask what kind of number you are holding. A minimum rounds up. A maximum rounds down. If you cannot tell, find the code section it came from and read whether it says “not less than” or “shall not exceed” — that sentence is the whole answer, and it is why every calculator here names the section it is applying.