Electricity bill from units consumed

One multiplication between the meter and the money

The relation is deliberately the simplest one in the cluster: units consumed times the price of a unit. The units are not a guess — they are the difference between two meter readings, and nothing says those readings must be a billing period apart. Read the meter this evening and again in a week and the difference is a week of the household’s life, priced immediately, at whatever moment curiosity strikes.

What the relation leaves out is the point of it. A real bill adds a standing charge, may tier the rate into slabs, and levies a percentage on top; this page models none of that, on purpose. What survives the stripping is exactly the marginal part — the money that moves when consumption moves — which is the only part worth consulting when the question is whether to change behaviour. The full structure, and why it makes small consumers pay the most per unit, is the fixed-charge page’s territory.

Run both directions against a real bill and the gap becomes diagnostic. Price your billed units here at the printed tariff and subtract the result from what you actually paid: the remainder is the structural cost of being connected — charges and levies no amount of switching off will touch. A household that has never separated the two parts tends to overestimate what conservation can do to the total.

The pack also declares the reverse workflow: fix an amount of money and the engine returns the units it buys at the tariff. In this slab-free relation that allowance is exact rather than naive, because there is no hidden structure being ignored — which makes it the right quick answer for prepaid metering and top-up questions, where money genuinely converts to units at a flat rate.

When this calculation is used

• Pricing a self-read interval — a week, a holiday absence, an experiment with a habit — from two meter photographs, without waiting for the utility.
• Converting a prepaid top-up to the units it buys, or the reverse, where a flat rate genuinely is the whole structure.
• Separating a real bill into its usage part and its structural part, by pricing the billed units here and comparing against the total actually paid.
• Solving backwards — the declared reverse workflow — from a spending figure to the consumption allowance it represents at your tariff.

Worked example

Price the pack’s anchor reading: a household that consumed three hundred and fifty units, at a tariff of fifteen hundredths per kilowatt-hour.

The engine returns the bill amount for those units alone. Set it beside the real bill for the same consumption and read the difference — that difference is the connection’s price, the part of the total that would remain if every switch in the house were off.

Then run the declared reverse: enter the money instead and let the engine return the units it buys. On a prepaid meter that is the literal meaning of a top-up; on a billed plan it is the consumption allowance a budget implies before the fixed charges take their share.

What each input represents

Assumptions and limits

• One flat rate prices every unit: tiered slabs, time-of-use windows and seasonal rates are outside this relation and need a blended rate to approximate.
• No fixed charge, levy or tax is modelled — deliberately. The figure here is the usage part of a bill, not the bill; the fixed-charge page carries the full structure.
• The relation is currency-agnostic: the tariff and the resulting amount share whatever unit of money the tariff was entered in.
• The units entered are an interval’s consumption, not a meter register — the arithmetic cannot tell a running total from a difference, so the reader must.

What the guards protect against

• Zero units consumed is refused — the pack ships that refusal as a declared test vector — because an interval in which the meter did not move has nothing to price, and returning zero would dress the absence of a question as an answer.
• Units are capped at a bound no household interval approaches, which catches the classic slip this page invites: a cumulative meter register entered where the difference between two readings belongs.
• The tariff is capped far above any retail rate, so a price entered in cents where currency per kilowatt-hour is expected — a hundredfold error — is refused instead of silently inflating the bill.

Provenance

Flat-rate billing relation, bill = units × tariff

The metered units are multiplied by the entered tariff to give the amount, with no slab, fixed-charge or tax structure applied; the declared reverse workflow divides a target amount by the same tariff to return the units it buys.

A reading aid for your own meter and bill, not billing advice — real utility bills add structure this relation strips by design. The number on the page is produced at load by the engine of a pack release whose signature is checked over its exact bytes first; the page states the verification outcome of the release it mounted, and the signed pack holds the citation.