How to Calculate Volume
Volume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.
Lena Hoffmann · 3 min read
Guides & tutorials
Practical guides, how-tos and comparisons to get the most out of our free online tools.
September 10, 2025
September 9, 2025
What an Investment Return Number Is Not Telling You
A fund can return 9.49 percent a year while its investor earns −1.77 percent. Time-weighted versus money-weighted, nominal versus real, gross versus net — four questions inside one number, separated with arithmetic.
Camille Laurent · 11 min read
How to Calculate the Square Metres of a Room
Find a room's area by multiplying length by width. Here's the method for rectangular, L-shaped and round rooms, and why area drives your material orders.
Marco Bianchi · 3 min read
September 8, 2025
Consolidating Debt Moves It, and Sometimes Costs More
Four balances of $20,000 at 20.6 percent blended, cleared on a $680 budget, cost $7,085 in interest. One loan at 9.9 percent over seven years cuts the payment to $330.99 — and costs $7,803. The break-even term is 77 months.
Camille Laurent · 10 min read
How to Calculate a Tip and Split the Bill
Multiply the bill by the tip percentage, add it on, then divide by the number of people. Here's the method, an example, and how tipping norms differ.
Camille Laurent · 2 min read
September 5, 2025
The 4 Percent Rule Is a Result From One Country and One Century
The rule is the output of a named backtest on US data. Its inversion, 1 ÷ w, gives the multiple: 25× at 4 percent, 33.3× at 3 percent. And two paths with the same 4.7676 percent geometric mean end one at zero and one at $2,031,661.
Camille Laurent · 12 min read
What Is a JWT (JSON Web Token)?
A JWT is a compact, signed token used to carry identity between services. Here's its three parts, how it's used for auth, and its security limits.
Daniel Okonkwo · 2 min read
September 4, 2025
Leverage, Liquidation, and the Asymmetry of Losses
Liquidation distance is (1 ÷ L − m) ÷ (1 − m): at 20× that is 2.56 percent on a 2.5 percent maintenance margin, inside a normal day. Recovering a loss needs 1 ÷ (1 − L) − 1, so 90 percent lost needs 900 percent back. Combined, repeated leveraged bets on a market with a genuine +0.08 percent edge compound at −1.23 percent per period at 10×.
Camille Laurent · 16 min read
September 3, 2025
Circle: Circumference and Area
Circumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.
Lena Hoffmann · 3 min read
September 2, 2025
Dollar-Cost Averaging: What It Actually Buys You
Spending a fixed amount each period buys more units when the price is low, so your average cost is the harmonic mean of the prices while the average price is the arithmetic mean — always lower, by 4.10 percent on the path worked through here. Against a lump sum, a 200,000-path simulation puts DCA's standard deviation 41 percent lower and its expected terminal wealth $337 lower on $12,000.
Camille Laurent · 14 min read
Volatility Is Not Risk, and the Square Root of Time Is a Choice
Annualised volatility = period standard deviation × √(periods per year), and that √t scaling assumes independent increments. It is a model, not arithmetic: at a daily autocorrelation of 0.1 a 60 percent annualised figure should read 66.3. The payload is volatility drag — the arithmetic mean exceeds the geometric by about σ²/2, so at 8 percent average return and 40 percent volatility the compound outcome is zero.
Camille Laurent · 15 min read
September 1, 2025
The Sharpe Ratio, and What It Quietly Assumes
Sharpe = (return − risk-free) ÷ standard deviation, so it prices return per unit of volatility — and volatility is symmetric. Two funds can share a Sharpe of 0.4939 while their Sortino ratios are 8.59 and 0.74. Annualising by √12 assumes independent returns: at an autocorrelation of 0.2 the published figure is 20 percent too high.
Camille Laurent · 15 min read