Methods and sources
How our tools calculate, round and handle the conventions that differ around the world, and where the numbers come from.
Our process
- Define the question precisely. Each tool starts from the questions people actually ask, including the awkward cases (a price that went down by more than 100%, a birthday on 29 February, a shift that ends after midnight).
- Use primary sources. Conversion factors and definitions come from standards bodies and legislation, listed below.
- Test. The calculation code is shared between the page's worked examples and the live tool, and is covered by automated tests with known answers, including edge cases such as zero, negative numbers, very large numbers, leap years and month ends. The worked examples and reference tables on each page are generated by the same code, so they cannot drift out of sync with the tool.
- Review. Every page shows the date it was last reviewed. Reported errors are checked against the source and fixed first.
Numbers you type
Number boxes accept both decimal points and decimal commas. "12.5" and "12,5" are both read as twelve and a half. A comma followed by exactly three digits, as in "1,500", is read as a thousands separator (one thousand five hundred), and the tool tells you when it has done so, so you can correct it. Spaces, apostrophes and thin spaces used as thousands separators are ignored. Results are always shown with a decimal point and comma grouping (1,234.5), a format that can be pasted back into any of our tools.
Rounding
- Calculations use full double-precision floating point. Nothing is rounded until the result is displayed.
- Money is shown to two decimal places, rounding halves up (away from zero), which is how most people and tills round. The unrounded value is shown in the working where it matters.
- Unit conversions are shown to 10 significant digits, enough to reveal when a conversion is exact (1 in = 2.54 cm) and far beyond the precision of any everyday measurement. Reference tables use fewer digits for readability.
- Percentages and averages show up to four decimal places, with trailing zeros removed.
- Very large or very small results switch to scientific notation (for example 1.5 × 10-9) rather than displaying as zero.
Units
The metric units are SI units or units accepted for use with the SI. US customary units follow the definitions published by NIST, including the international yard and pound of 1959 (1 yd = 0.9144 m exactly, 1 lb = 0.45359237 kg exactly). The US liquid gallon is 231 cubic inches (3.785411784 L). The imperial gallon used in the United Kingdom is 4.54609 L exactly, as defined in the UK Weights and Measures Act 1985. Cups and spoons differ by country, so the tools label them explicitly: the metric cup (250 mL), the US customary cup (about 236.6 mL) and the US nutrition-labeling cup (240 mL).
Dates and times
- Dates are calculated as whole calendar days, with no time of day, so daylight-saving changes cannot shift a result.
- All dates use the Gregorian calendar, extended backwards before its adoption (the "proleptic" Gregorian calendar, as in ISO 8601). Years 1 to 9999 are supported.
- Adding months keeps the day of the month where possible. When that day does not exist (31 January + 1 month), the result moves back to the last day of the month (28 or 29 February), and the tool says so.
- "Today" comes from your device's clock and time zone.
- Weekends are configurable because they differ: Saturday and Sunday in most countries, Friday and Saturday in several Middle Eastern and North African countries, and only one day in some places. Public holidays are not included because they vary by country, region and year.
- Dates in results are written as "Thursday, 29 February 2024", a format that cannot be misread in countries that write dates day-first or month-first.
Text
- Words are counted as runs of letters or numbers. An apostrophe, hyphen or full stop between letters or digits keeps them together, so "don’t", "well-known" and "3.14" each count as one word.
- Characters are counted as user-perceived characters (Unicode grapheme clusters), so an emoji or an accented letter counts once. Code-unit and byte counts are shown separately for systems with technical limits.
- Reading time uses an average adult silent reading rate of 238 words per minute and a speaking rate of 183 words per minute, from Brysbaert's 2019 meta-analysis. Individual speeds vary widely.
- Text you enter is processed only in your browser.
Sources
- 3GPP TS 23.038: Alphabets and language-specific information, 3GPP
- Approximate Conversions from U.S. Customary Measures to Metric, NIST
- Brysbaert, M. (2019). How many words do we read per minute? A review and meta-analysis of reading rate. Journal of Memory and Language, 109, PsyArXiv preprint
- Directive 98/6/EC on consumer protection in the indication of the prices of products, EUR-Lex
- Guidelines for Determining Metric Equivalents of Household Measures, U.S. Food and Drug Administration
- Hours worked and "off the clock" work under the Fair Labor Standards Act, U.S. Department of Labor, Wage and Hour Division
- ISO 8601 Date and time format, International Organization for Standardization
- NIST/SEMATECH e-Handbook of Statistical Methods: Measures of Location, National Institute of Standards and Technology
- NIST/SEMATECH e-Handbook of Statistical Methods: Measures of Scale, National Institute of Standards and Technology
- The International System of Units (SI Brochure), 9th edition, Bureau International des Poids et Mesures (BIPM)
- Unicode Standard Annex #29: Unicode Text Segmentation, Unicode Consortium
- Unit Conversion (SP 811 Appendix B factors and Handbook 44 Appendix C tables), National Institute of Standards and Technology (NIST)
- Weights and Measures Act 1985, Schedule 1 (definitions of imperial units), legislation.gov.uk