How totals are calculated

You enter amounts at whatever frequency you actually receive or pay them — weekly, every two weeks, monthly, or yearly. Those numbers cannot be added together as they stand: a weekly $100 and a yearly $100 are nothing like the same amount of money. So Longhand converts every entry to one common monthly basis first, adds the monthly figures together, and then re-expresses the total at whichever period you have selected.

This page states that conversion exactly, so you can check any figure the app shows against your own arithmetic.

The conversion factors

Every amount is first converted to a monthly figure:

weekly → × 52 ÷ 12 (about 4.3333 times a month)
every two weeks (shown as Bi-weekly in the app) → × 26 ÷ 12 (about 2.1667 times a month)
monthly → × 1
yearly → ÷ 12

The factors come from the calendar, not from a rule of thumb: there are 52 weeks and 26 fortnights in a year, and 12 months. The familiar "about 4.33 weeks in a month" is the result of 52 ÷ 12, not the definition.

To show a total at any period other than monthly, the monthly figure is converted back by the inverse of the same factor:

yearly = monthly × 12
weekly = monthly × 12 ÷ 52
every two weeks = monthly × 12 ÷ 26
monthly = the monthly figure itself

That is why the period selector never changes what you entered, only how it is expressed. Your entries are kept exactly as you typed them, at the frequency you chose; the monthly figure is worked out from them each time a total is shown.

The same maths as your spreadsheet

If you already keep a budget spreadsheet, this is the same arithmetic you are already doing. Each of these pairs is algebraically identical:

a yearly amount as a weekly figure: yearly ÷ 52
a monthly amount as a weekly figure: monthly × 12 ÷ 52
an every-two-weeks amount as a monthly figure: every two weeks ÷ 2 × 52 ÷ 12

So if one of your figures disagrees with Longhand's, the two are not using different conversion models. Check the entries themselves — a missing row, a duplicate, or an amount recorded at the wrong frequency — rather than looking for a different formula. If the gap is only a few cents and every entry checks out, it is the rounding described further down this page, not a mistake.

A worked example

Three income entries at three different frequencies:

Salary     $2,000.00  every two weeks  →  2,000.00 × 26 ÷ 12  =  $4,333.33   (from 4,333.333…)
Freelance    $600.00  a month          →  600.00 × 1          =    $600.00
Dividend   $1,200.00  a year           →  1,200.00 ÷ 12       =    $100.00
                                       Monthly total          =  $5,033.33

Shown at the yearly view:  5,033.33 × 12                      = $60,399.96
Same figures in a spreadsheet: 2,000×26 + 600×12 + 1,200      = $60,400.00
                                                    difference =       4¢

Every figure there is what Longhand actually renders for those three entries.

Why a few cents go missing

The four-cent gap above is not an error, and it has two separate causes worth telling apart.

Each entry is rounded to the nearest cent as it is converted to its monthly figure. The salary row above converts to $4,333.333…, which becomes $4,333.33 — a third of a cent is dropped there and then. Over a long list those fractions add up, so a total can end up a few cents away from what you would get by rounding only once at the very end. The scale is small and bounded: under half a cent per entry at the monthly view, and under about six cents per entry at the yearly view (that half-cent, multiplied by 12).

A breakdown is rounded separately from the total above it. A category breakdown adds up figures that have each been rounded already, while the headline total is rounded once over everything. At the weekly and every-two-weeks views — the two whose factors are not whole numbers — those two routes can land a cent or two apart. At the monthly and yearly views they agree exactly, which is why you only see that note on the other two. Where a breakdown can differ from the total beside it, Longhand says so on the page rather than leaving you to find it.

This is also why a single $100.00 yearly entry shows as $99.96 at the yearly view: $100.00 ÷ 12 is $8.333…, which becomes $8.33, and $8.33 × 12 is $99.96. The four cents are the rounding, not a lost payment. Longhand rounds this way on purpose, and always from the same monthly figure, so a total is never quietly recomputed a second way — the few cents you see are the ones described here.

Still have a figure you cannot reconcile? Reach us through the contact form, or see the FAQ for the shorter version of this explanation.