Methodology
Which formulas the calculators use, how results are rounded, where the arithmetic has known limits, and how the pages on this site are written and checked.
The formulas behind each tool
Nothing on this site uses a proprietary method. Every result comes from standard arithmetic that you can reproduce on paper, and the step-by-step working under each answer shows exactly which operations were applied to your numbers.
| Tool | Formula used |
|---|---|
| Percent of a number | base × (percent ÷ 100) |
| What percent X is of Y | (part ÷ whole) × 100 |
| Increase or decrease | base × (1 + percent ÷ 100) |
| Percentage change | ((new − old) ÷ old) × 100 |
| Discount | price × (1 − discount ÷ 100) |
| Tip | bill × (percent ÷ 100) |
| VAT, adding | net × (1 + rate ÷ 100) |
| VAT, removing | gross ÷ (1 + rate ÷ 100) |
| Profit margin | ((revenue − cost) ÷ revenue) × 100 |
| Salary raise | ((new − old) ÷ old) × 100 |
| Real raise after inflation | ((1 + raise ÷ 100) ÷ (1 + inflation ÷ 100) − 1) × 100 |
| Percentage points | second − first |
| Relative change | ((second − first) ÷ first) × 100 |
| Percentage difference | |second − first| ÷ ((first + second) ÷ 2) × 100 |
Each calculator also solves its formula in reverse when you leave a different field empty. The inverse of a multiplication is a division, not a subtraction, which is the single most consequential thing this site tries to make visible.
Rounding and precision
- Answers are rounded to two decimal places and a trailing ".00" is removed, so 30.00 displays as 30.
- Intermediate values in the step-by-step working are shown to up to six decimal places, so that each line is consistent with the next.
- Rounding happens only at display time. The arithmetic itself runs on unrounded values, so chained operations do not accumulate display error.
- Percentages are not clamped to any range. A result above 100% or below zero is shown as calculated, because both are meaningful in several of these contexts.
Floating point
Calculations use the IEEE 754 double-precision arithmetic built into every browser and spreadsheet. Some decimal fractions cannot be represented exactly in binary, which is why 0.1 + 0.2 famously does not equal 0.3 in almost every programming language. At two decimal places of display this is invisible, but it is a real property of the arithmetic rather than a bug in this site.
What this means for accounting
Tax and invoicing rules usually specify where rounding must occur — per line item, per invoice, or per tax rate — and the required answer can differ by a unit from a single rounded calculation. Use the displayed figure as a check, not as the entry, and apply your own jurisdiction's rounding rule at the step it names.
Reference data on this site
Some pages carry reference tables that are not derived arithmetic but observed figures — VAT rates by country, tipping conventions, typical margin ranges. These are compiled from public government and industry sources and are provided as orientation rather than as authority.
- Tax rates change, often with little notice, and most jurisdictions operate reduced rates alongside the standard one. Confirm the current rate with the relevant tax authority before invoicing.
- Tipping conventions are social rather than legal, vary within a country, and shift over time. The ranges given describe common practice, not a rule.
- Nothing on this site is financial, tax, accounting or legal advice. The arithmetic is only one input into decisions that usually depend on rules specific to your circumstances.
How pages are written and checked
Pages are written by hand rather than generated. Every worked example on the site was calculated and checked against the tool it appears next to, and the numbers in the tables were recomputed rather than copied from elsewhere.
Each page carries a "last reviewed" date at the foot. That date changes when the substance of the page changes — a corrected figure, a rewritten section, a new table — and not for typographical fixes. The same date is published in the page's structured data and in the site's sitemap, so all three agree.
Corrections
If a result or a stated figure is wrong, it gets fixed. Reports go to franfactory.store@gmail.com; including the numbers you entered and the answer you expected is usually enough to reproduce the problem the same day. Corrections to substance are made in place and the review date is updated.
Translations
The English and Portuguese versions of each page are written as parallel texts rather than machine-translated, and the worked examples are checked in both. Where a locale does not yet have a page, its links point to the English version rather than to a stub.
Frequently Asked Questions
- How are the results rounded?
- To two decimal places for display, with trailing zeros removed. The underlying arithmetic is unrounded, so chained calculations do not accumulate display error.
- Why does the working show more decimal places than the answer?
- So that each line follows from the one before it. Rounding an intermediate value to two places would sometimes make the final multiplication look wrong.
- Can I rely on these figures for an invoice?
- Use them as a check. Tax rules specify where rounding must occur, and the required entry can differ by a unit from a single rounded calculation.
- Where do the VAT rates and tipping customs come from?
- Public government and industry sources, compiled for orientation. Rates change and conventions vary, so confirm anything that matters with the relevant authority.
- What does the "last reviewed" date mean?
- The page was read through and its figures checked on that date. It changes when the substance changes, not for typographical fixes.
Last reviewed