Emergency fund calculator — methodology

Runway, and why it is the headline rather than a target

runway  = fund ÷ essential monthly spending
target  = essential monthly spending × months you chose
gap     = max(0, target − fund)

Runway asserts nothing. It is a division, it uses only figures the reader supplied, and it is the same number whatever anybody thinks the right target is. With no spending entered there is no runway and the page shows a dash — not the infinity the division produces, and not a zero, because neither is true.

The target is a second and separate input, and four targets are shown side by side underneath the answer. That is a layout decision carrying an argument: a page that showed one row would be making a recommendation through its design that its copy declines to make in words.

A year of interest, and a year of borrowing cost

interest         = fund × savings rate
borrowing cost   = gap  × borrowing rate
gain on a sale   = gap  × the share of a sale that is profit

Simple, over one year, with nothing compounded. An account quoting an AER already carries its within-year compounding inside the quoted rate, and a credit APR likewise, so a single multiplication is the year’s figure for a balance left alone. The borrowing figure is what a balance costs to carry for twelve months, not a repayment schedule: paying it down faster costs less and paying the minimum costs more, and neither is modelled.

The tax on the interest is measured, not read off an allowance

tax on the interest = tax(income, interest) − tax(income, no interest)

Two engine calls and a subtraction. This is not the same as adding up the tax on the savings bands, and the difference is not rounding: the personal allowance is allocated across income types in whatever way produces the lowest bill, so taking the interest away changes that allocation and some of the cost of receiving it lands on the earned income underneath. On £50,000 of earnings with £1,000 of interest, in 2026/27, the banded figure is £92.00 and the measured cost is £146.00.

An allowance with room left in it is not a promise of tax-free income, and this page never captions it as one. The personal savings allowance is £1,000, £500 or nothing according to the band the taxpayer reaches — and the interest itself counts towards deciding that band, so the interest the row appears to invite can be the thing that halves the row. What sits next to the allowance table is therefore the measured cost of another £100 of interest, which answers the question the reader was really asking.

The fund at which the tax starts

This is the figure a reader with a growing cash pot actually wants, and it is not the allowance divided by the rate. Three things sit between them: the personal allowance, if there is any of it spare; the starting rate for savings, which is reduced pound for pound by non-savings taxable income; and the personal savings allowance, which steps down with the band. Adding the headline figures together gets the wrong answer for most people in the middle.

taxed(interest) = tax(income, interest) > tax(income, no interest)

bisect for the smallest whole pound of interest where taxed() is true
fund = that interest ÷ the savings rate, rounded up

Income tax is non-decreasing in savings income, so “is this interest taxed” is a monotone predicate and halving the interval is exact rather than approximate. The upper bound of the search is provable rather than guessed: at the personal allowance plus the starting rate band plus the largest personal savings allowance, plus one pound, a taxpayer with no other income at all has a pound of savings income above every nil-rate band there is, and any other income only brings that point closer. If even that costs nothing there is nothing to find, and the page says so rather than printing a figure.

Rates and allowances

Savings interest is taxed on the UK-wide bands wherever the saver lives, so the region selector changes this answer only through the band the earnings put them in. Capital gains tax is not devolved either.

Sources

• gov.uk — Tax on savings interestThe personal savings allowance by band, and the starting rate for savings that sits underneath it.
• gov.uk — Individual Savings Accounts (ISAs)That interest inside an ISA is not taxed, and the annual subscription limit that using one consumes.
• gov.uk — Capital gains tax rates and annual tax-free allowancesThe annual exempt amount and the rates that price a forced sale of investments.
• gov.uk — Income Tax rates and allowances: current and pastThe personal allowance and the band thresholds, which decide which personal savings allowance applies.

Four things that change the answer and are not modelled

• What your essential spending really is. Everything here scales off one figure, and the most common way this calculation goes wrong is entering ordinary monthly outgoings rather than the ones that continue with no income. Subscriptions, holidays, saving and most discretionary spending stop when the income does, and including them overstates the fund needed — sometimes by half.
• What else you could fall back on. Statutory redundancy pay, contractual notice, a partner’s income, income protection or critical illness cover, and benefit entitlements all reduce the fund required and none of them is an input here.
• What markets do. The larger cost of a forced sale is that it happens when the emergency happens, which is frequently after prices have already fallen. There is no market model on this page and there should not be one: what is priced is the capital gains tax, because that is the part that can be counted, and the rest is the reason for holding cash rather than a number this calculator can produce.
• Time. One year of simple interest at the rate you typed. Nothing is compounded, no term is run and no rate is assumed to persist, so nothing here is a forecast and none of it is presented as one.