How the calculators work

This page explains how every calculator on dash-calculator.com works, so you know what the numbers mean and when to check them twice.

1. One standard formula per calculator

Each calculator uses the standard formula for its question, the one found in a textbook or a reference handbook. The page writes it out in words and symbols, defines every variable with its unit and works an example with the default numbers. Unit factors are exact by definition (1 in = 2.54 cm, 1 ft = 0.3048 m, 1 US fl oz = 29.5735 mL, 1 yd = 36 in) and are stated where they are used.

2. Inputs, units and conventions

• Every input shows its unit at the end of the box. Enter numbers in that unit, or use the unit converter first.
• Thousands separators (1,250) and decimal points (12.5) are both fine.
• Angles are in degrees unless the input says radians. Polar and spherical angles follow the convention printed on each page (for spherical coordinates, θ is the azimuth and φ the angle from the z-axis).
• Inputs have sensible limits: a length cannot be negative and a modulus must be at least 1. Outside the limits the calculator explains what it needs.
• Figures that change from product to product, such as a fabric width or a carton size, are inputs, never assumptions. Take them from the label.

3. How results are calculated and rounded

• Sums run in full double precision and are rounded only for display. Each result keeps the decimals shown in the page’s “Rounding” line, and gains decimals when a small number would otherwise round away.
• Counts you have to buy (fabric widths, cartons) are rounded up to whole units.
• Durations are shown as m:ss or h:mm:ss, rounded to the nearest second.
• If a result cannot be computed (a division by zero, the square root of a negative number), the calculator says “Cannot compute” instead of showing a misleading number.

4. Checking a result

Every calculator has a worked example that uses the default numbers and shows each step. The “Formula used” box lists the exact lines the calculator runs. A small chart shows how the main result changes when the first input moves between half and one and a half times your value, with a table you can open.

5. Limits

A formula is a model. Angles follow stated conventions, belts slip, fabric shrinks and products differ. Each page lists the limits that matter for its formula. Results are estimates for planning, not professional advice; see the disclaimer.

6. Errors and corrections

If a result looks wrong, send the page’s address and the numbers you entered through the contact page. Confirmed errors are fixed and listed on the corrections page. A calculator under review can be switched off while its formula stays visible.