A natural gas bill measures one thing and charges for another, and the conversion between them is printed on the bill.

The units
CCF — one hundred cubic feet. This is what the meter measures, because a meter measures volume.
Therm — 100,000 BTU. This is energy, and it is what the bill charges for.
MCF — one thousand cubic feet, used by some utilities.
The conversion between volume and energy is the BTU factor or heating value, printed on the bill and typically around 1.03. One CCF is therefore about 1.03 therms, and it varies slightly with the composition of the gas being delivered.
What is on the bill
A customer or basic charge, fixed each month regardless of usage.
Delivery or distribution charges, usually per therm, for moving the gas through the local network.
Supply or commodity charge, the cost of the gas itself, per therm. In deregulated markets this can be purchased from a third party.
Taxes and surcharges.
The fixed portion matters when comparing months. A summer bill is mostly fixed charges plus water heating and cooking; a January bill is mostly heating. Comparing the totals overstates the ratio between them.
Estimated readings
Many utilities estimate the meter in some months and read it in others.
An estimated month followed by an actual read produces a correction, which is why one bill sometimes looks anomalous and the next one explains it. A bill marked estimated is not a measurement, and it is not a basis for concluding anything about the furnace.
Most utilities accept a customer reading, and submitting one before a cold-season estimated period avoids the confusion entirely.
Isolating the heating
Take a summer month — a month with no heating — as the baseline. That is water heating, cooking and the fixed charges.
Subtract it from a winter month. The difference is very close to the heating usage.
Doing this makes a comparison between two winters meaningful, because it removes the constant load and the fixed charges from both sides.
Normalising for the weather
Divide the heating therms by the heating degree days for the same period, which most utilities print on the bill or which NOAA publishes by station.
The result is therms per degree day, and it is comparable across seasons.
A stable figure means the furnace and the house are behaving the same and the bill moved with the weather. A rising figure means something has changed.
Converting to cost per BTU
To compare gas against another fuel:
$ per million BTU = (price per therm ÷ 100,000) × 1,000,000 ÷ AFUE
Use the all-in price per therm — total bill minus fixed charges, divided by therms — rather than the headline commodity rate, which is only part of what is actually paid.
What a sudden increase usually is
In order of likelihood: colder weather, an estimated reading correction, a rate change, a thermostat setting change, a furnace losing efficiency, and a leak.
The degree-day calculation distinguishes the first from the rest in about five minutes, which is worth doing before calling anyone.
Keeping the record
Two columns — therms and degree days — for each billing period.
After two winters that table answers questions that no single bill can, and it is the evidence that shows whether insulation or a new furnace actually changed anything.
Deregulated markets and supplier offers
Where the supply portion can be bought from a third party, the offers are for the commodity only — delivery charges and fixed charges stay with the utility regardless.
That means a headline rate advertised as a large saving applies to part of the bill, not the whole of it. Work out the utility's own all-in price per therm from a recent bill first, then compare.
Fixed-rate contracts trade a higher average price for predictability, which is worth something in a house with a large heating load and worth very little in a mild climate where winter bills are small either way.
Budget billing
Many utilities offer a levelised monthly payment based on the previous year's usage, trued up annually.
It smooths cash flow and it hides the seasonal signal completely, so a household on budget billing should track therms rather than dollars if it wants to notice anything changing.
