Calculation & Conversion Cheat Sheet
Percentages, compound interest, statistics, unit conversion — simple on the surface, yet the same traps recur: a base that moved, a metric that mismatched, a unit that slipped. This page tabulates six common calculations by purpose, use case and pitfall, with anchor points for all three temperature scales.
Six Common Calculations
| Calculation | What It Does | Typical Use | Common Pitfall |
|---|---|---|---|
| Percentage | Share, increase/decrease, original and discounted price | Discounts, growth rates, completion rates | +50% then −50% does not return to the original; the base changed |
| Expression Evaluator | Evaluate expressions with brackets and functions | Quick checks, applying a formula repeatedly | Mind operator precedence and degrees versus radians |
| Statistics | Mean, median, mode, variance and standard deviation | Central tendency and spread of a dataset | The mean is dragged by outliers; use the median for skewed data |
| Compound Interest | Interest on interest per period, optionally with regular contributions | Deposits, loans, recurring investment returns | Nominal APR is not the effective annual rate; check compounding frequency |
| Unit Converter | Convert length, mass, area, volume, speed and more | Cross-border documents, engineering drawings, recipes | US and imperial gallons and ounces differ; confirm the system first |
| Temperature | Convert between Celsius, Fahrenheit and Kelvin | Oven settings, weather reports, lab records | Temperature is an interval quantity, not a ratio one; do not scale it directly |
Temperature Anchor Points
Formulas: °F = °C × 9/5 + 32 and K = °C + 273.15. The table lists anchor points that are easy to memorise.
| Reference Point | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| Water freezes | 0 | 32 | 273.15 |
| Room temperature | 20 | 68 | 293.15 |
| Body temperature | 37 | 98.6 | 310.15 |
| Water boils | 100 | 212 | 373.15 |
| Moderate oven | 180 | 356 | 453.15 |
Frequently Asked Questions
Why does +50% followed by −50% not return to the original price?
Because the two calculations use different bases. Starting from 100, a 50% rise gives 150. A 50% fall then removes half of 150, which is 75, leaving 75 — a loss of 25. Whenever equal percentage moves are applied in opposite directions the result is always below the starting point, and the shortfall equals the square of the change (here 0.5 × 0.5 = 0.25, a 25% loss). Falling first and rising second produces the identical loss.
Should I report the mean, median or mode?
It depends on the distribution. Use the mean when the data is roughly symmetric with no outliers, since it uses every data point. Use the median when outliers or strong skew are present — income, house prices and response times are classic cases — because it resists extreme values and better represents the typical case. Use the mode for categorical data or when you need to know the most common value, such as the best-selling size. A useful habit: report the mean together with the median so readers can immediately judge whether the data is skewed.
Why do nominal APR and effective annual return differ?
The difference comes from compounding frequency. A 12% nominal APR compounded monthly means 1% per month; after a year that is 1.01 to the twelfth power, about 1.1268, so the effective annual rate is 12.68%, not 12%. The more frequent the compounding, the higher the effective rate; with continuous compounding it approaches e to the power r minus one. Always compare products on the effective annual basis — the nominal rate alone is misleading.
Why does converting Celsius to Fahrenheit also add 32?
The two scales have different zero points and different degree sizes. Celsius sets the freezing point of water at 0 and boiling at 100, split into 100 equal parts. Fahrenheit sets freezing at 32 and boiling at 212, split into 180 parts. A Fahrenheit degree is therefore 100/180, or 5/9, of a Celsius degree. Converting requires scaling by 9/5 first and then shifting by 32 to align the zeros: °F = °C × 9/5 + 32. Kelvin simply moves the zero to absolute zero while keeping the Celsius step size, so you only subtract 273.15.