Practical guides, how-tos and comparisons to get the most out of our free online tools.
The DPI figure inside an image file is a label. It changes no pixels. Printed size is pixels divided by PPI — and DPI, properly used, means something else entirely: the printer's dots.
Daniel Okonkwo · 10 min read
The USDA's figure of 233,610 dollars for a middle-income child born in 2015 — 317,315 restated in 2025 money — is not a sum of receipts. It is allocated household spending, and the housing line is measured as the cost of one more bedroom.
Camille Laurent · 12 min read
Two properties decide the format — photographic or flat-toned, and whether it needs alpha or animation. Everything else is downstream. With measured byte counts for the same two images in all four formats.
Daniel Okonkwo · 13 min read
PV = FV ÷ (1+r)^n. At 7 percent over 30 years the discount factor is 0.131, so a promise of $100,000 in thirty years is worth $13,137 today — and $41,199 if you assume 3 percent instead.
Camille Laurent · 7 min read
PV = nRT holds when the gas is dilute and far from condensing. The value of R depends entirely on the units you feed it, and the temperature is never in degrees Celsius.
Lena Hoffmann · 7 min read
IRR picks the $10,000 project returning 50 percent; NPV picks the $100,000 project returning 30 percent, worth $20,370 against $3,889. And a mine with a cleanup cost has two IRRs, 10 and 20 percent, so the rate answers nothing.
Camille Laurent · 7 min read
EMI = P·i·(1+i)^n ÷ ((1+i)^n − 1). On $300,000 at 6 percent, doubling the term from 15 to 30 years cuts the payment by 29 percent but multiplies the interest by 2.2 — from $155,683 to $347,515.
Camille Laurent · 7 min read
The stop goes where your idea is wrong, not where your comfort runs out — and then the position size adapts to it. Here is the volatility argument, the sizing arithmetic, and the win rate each reward multiple demands.
Camille Laurent · 9 min read
Split a bill and tip evenly across a group. Learn the tip percentage, total, and per-person formulas with a clear worked example so nobody over- or underpays.
Lena Hoffmann · 3 min read
Estimate your retirement age from how many years it takes your savings to reach a target. Learn the growth formula, a worked example, and why the target matters most.
Lena Hoffmann · 4 min read
Life expectancy is an actuarial average by age and sex, not a personal prediction. Learn how life tables work, why the figure rises as you age, and how to read the numbers.
Lena Hoffmann · 4 min read
Funding is paid every eight hours on the full notional, between traders rather than to the exchange. A rate of 0.01 percent looks like nothing and costs 10.95 percent a year. Here is the formula and an annualised table.
Camille Laurent · 7 min read