What's the difference between percentage change and percentage difference?
Percentage change is directional — it measures how much one value changed relative to the original. Percentage difference is symmetric — it measures the difference relative to the average of the two values, with no "before" or "after." Use % change for before/after comparisons (price changes, growth rates) and % difference when comparing two equal peers.
How does the random number generator work?
It uses the browser's built-in Math.random() function, which produces cryptographically unpredictable results in modern browsers. When "Unique only" is selected, a Fisher-Yates shuffle algorithm ensures no duplicates. All numbers are generated entirely on your device — nothing is sent to a server.
How fair are the dice rolls?
The dice roller uses Math.random() which produces a uniform distribution over [0, 1). Each die face has exactly equal probability. Over many rolls, results converge to the expected distribution. It's as fair as any physical die — the expected average for a d6 is 3.5.
What number bases are supported in the converter?
The base converter supports Decimal (10), Binary (2), Hexadecimal (16), Octal (8), and any Custom Base from 2 to 36. For bases above 10, it uses digits 0–9 plus letters A–Z. Enter a number in any base and see all conversions simultaneously. Binary output also shows nibble (4-bit) grouping and bit-length classification.
What is the valid range for Roman numerals?
Standard Roman numerals represent integers from 1 to 3,999 (I to MMMCMXCIX). Numbers outside this range cannot be expressed with the traditional seven symbols. The Year Mode is a convenient way to convert historical dates and copyright years directly.
How does the Number Properties tool determine if a number is prime?
It uses trial division up to √n. For any composite number n, at least one factor must be ≤ √n, so checking up to that point is sufficient. For numbers up to 10,000,000, this requires at most ~3,162 division operations — nearly instant in JavaScript.
What does "abundant" vs "deficient" mean?
These classify a number by the sum of its proper divisors (all divisors excluding the number itself). A number is abundant if the sum exceeds it (e.g., 12: 1+2+3+4+6=16 > 12), deficient if the sum is less (e.g., 9: 1+3=4 < 9), and perfect if the sum exactly equals it (e.g., 6: 1+2+3=6). About 75% of all integers are deficient.
Can I share my calculation with someone?
Yes! Click the "Share" button on any tab. This copies a URL that encodes all your current inputs. When someone opens the link, the tool restores exactly the same values so they can see your calculation. Your inputs are also automatically saved to localStorage so they persist across page reloads.
Is my data sent anywhere?
No. All calculations run 100% in your browser using JavaScript. Nothing is uploaded to a server. You can even use most features offline after the page loads (only Chart.js loads from a CDN on first visit).