toolsapp

How our calculators work

Every tool on toolsapp.work implements one published method, shows that method on its page, and runs entirely in your browser. This page lists the formulas, unit definitions and standards behind all 42 tools.

Last reviewed

How we check a formula

  1. Pick the source. We use the defining standard where one exists (SI unit definitions, WHO categories, RFCs for encodings) and the original paper for equations such as Mifflin-St Jeor or Tanaka.
  2. Implement it once. All 42 tools share one calculation engine, so a formula is written in one place and every page that uses it gets the same result.
  3. Test against worked examples. Results are compared with the examples in the source, with hand calculations and with edge cases such as zero, negative and very large inputs.
  4. Show the working. Each tool page prints its formula under the result, so you can repeat the calculation yourself.
  5. Fix reports quickly. If a result looks wrong, email support@toolsapp.work with the inputs and we will check it against the source.

Math line

  • Basic Calculator and Scientific Calculator: standard order of operations (brackets, powers, multiplication and division, addition and subtraction), with implicit multiplication such as 2π. A percent after an added or subtracted term means a percent of the running total, so 200 + 15% = 230.
  • Arithmetic uses IEEE 754 double precision, accurate to about 15 significant digits. Trigonometry works in degrees or radians; factorials are exact up to 170!.
  • Percentage Calculator: X% of Y = X ÷ 100 × Y; percent change = (new - old) ÷ |old| × 100.
  • Circumference Calculator: C = 2πr = πd and A = πr².
  • Date Calculator: counts calendar days from the start date up to the end date; weekdays exclude Saturdays and Sundays.

Health line

  • BMI Calculator: BMI = weight (kg) ÷ height (m)², with the World Health Organization adult categories: under 18.5 underweight, 18.5 to 24.9 healthy, 25 to 29.9 overweight, 30 or more obesity.
  • Calorie Calculator: Mifflin-St Jeor resting energy, BMR = 10 × weight (kg) + 6.25 × height (cm) - 5 × age + 5 for men or - 161 for women, multiplied by an activity factor from 1.2 to 1.9.
  • Body Fat Calculator: U.S. Navy circumference method (Hodgdon and Beckett), using log10 of waist minus neck (men) or waist plus hip minus neck (women) and height; results are classified with the ACE body fat categories.
  • Heart Rate Calculator: maximum heart rate = 208 - 0.7 × age (Tanaka), training zones by the Karvonen method: target = resting + intensity × (maximum - resting).
  • Protein Calculator: 0.8 to 2.4 g per kg of body weight depending on goal, following sports-nutrition position stands.
  • Water Intake Calculator: 33 ml per kg of body weight, plus 350 ml per 30 minutes of exercise and 500 ml in hot weather.

Money line

  • Mortgage Calculator and Loan Calculator: fixed-rate amortization, M = P × r ÷ (1 - (1 + r)^-n), where r is the annual rate divided by 12 and n the number of monthly payments. Extra payments go to principal.
  • Investment Calculator: monthly compounding, balance each month = previous balance × (1 + r) + contribution.
  • Retirement Calculator: the same growth model, converted to today's money by dividing by (1 + inflation)^years, with income estimated by the 4% withdrawal rule (Bengen).
  • Budget Calculator: the 50/30/20 rule, 50% needs, 30% wants and 20% savings and debt repayment.
  • Debt Payoff Calculator: months to repay = -ln(1 - r × balance ÷ payment) ÷ ln(1 + r).
  • Currency Converter: daily mid-market reference rates from an open exchange-rate dataset. Banks and card networks add their own margin, so the amount you receive will differ.

Converters line

  • Exact definitions from the International System of Units and NIST: 1 in = 2.54 cm, 1 ft = 0.3048 m, 1 mi = 1,609.344 m, 1 lb = 0.45359237 kg, 1 oz = 28.349523125 g.
  • Temperature: °F = °C × 9/5 + 32 and K = °C + 273.15.
  • Energy and power: 1 cal = 4.184 J, 1 kWh = 3.6 MJ, 1 BTU = 1,055.06 J, 1 mechanical horsepower = 745.7 W.
  • Pressure and area: 1 atm = 101,325 Pa, 1 psi = 6,894.757 Pa, 1 acre = 4,046.8564224 m².
  • Cooking uses US customary measures: 1 cup = 236.588 ml, 1 tablespoon = 14.787 ml. Data size uses decimal units (1 KB = 1,000 bytes) and binary units (1 KiB = 1,024 bytes) as defined by the IEC.
  • Results show up to seven significant digits.

Digital line

  • Hash Generator: SHA-1, SHA-256, SHA-384 and SHA-512 from the browser's Web Crypto API (FIPS 180-4); MD5 per RFC 1321 for checksums only.
  • Password Generator: characters drawn with crypto.getRandomValues using rejection sampling, so every character is equally likely; strength is shown as entropy = length × log2(pool size).
  • Base64 Converter: RFC 4648 Base64 of the text's UTF-8 bytes, with the URL-safe alphabet as an option. URL Encoder: percent-encoding as specified by RFC 3986.
  • JSON Formatter: validated with the browser's standard JSON parser (RFC 8259) and re-serialised with your chosen indent.
  • QR Code Generator: QR codes per ISO/IEC 18004 with error correction levels L, M, Q and H.
  • Color Picker: contrast ratios from the WCAG 2 relative-luminance formula.

Time & Text line

  • Timezone Converter: offsets and daylight saving rules from the IANA time zone database built into your browser.
  • Pomodoro Timer, Countdown Timer and Stopwatch: timed against the browser's monotonic clock, so they stay accurate in background tabs.
  • Work Schedule Calculator: daily hours = end - start - unpaid break, with overtime paid at 1.5 times the hourly rate above your weekly threshold.
  • Word Counter: reading time at 238 words per minute (Brysbaert, 2019) and speaking time at 150 words per minute.

Sources

Limitations

  • Health results are population estimates for healthy adults. They are not a diagnosis; speak to a doctor about your own health.
  • Financial results ignore taxes, fees and lender-specific rules unless you enter them. Use them to compare options, not as a quote.
  • Calculator results are rounded to 12 significant digits for display, so the last digit of a very long result can differ from exact arithmetic.
  • Exchange rates update daily, so they will not match live trading prices.