Exponential Regression Calculator
Last reviewed 12 September 2026
Counts the rows dropped because y was not positive instead of discarding them silently, and states which noise model each fitting objective corresponds to — lognormal multiplicative error for the linearised fit, additive normal for the other — so the choice is stated rather than made by whichever tool was opened.
Burn Rate Calculator
Last reviewed 12 September 2026
Separated gross burn from net burn and verified that runway follows net burn, so revenue is not double-counted against the cash balance.
Net Profit Calculator
Last reviewed 12 September 2026
Tested the full waterfall for internal consistency: revenue less cost of goods, operating expenses, interest and tax must reconcile to net profit at every step.
Return on Equity Calculator
Last reviewed 12 September 2026
Verified the DuPont identity directly — return on assets multiplied by the equity multiplier reproduces return on equity — so the decomposition shown cannot disagree with the headline ratio.
Return on Assets Calculator
Last reviewed 12 September 2026
Verified the DuPont split: net margin multiplied by asset turnover reproduces return on assets exactly.
GDP per Capita Calculator
Last reviewed 12 September 2026
Property-tested that output per head scales inversely with population, and documented the units trap: GDP in billions against population in millions.
GDP Growth Rate Calculator
Last reviewed 12 September 2026
Tested that growth is measured against the starting period and that the absolute change reconciles to the rate.
GDP Deflator Calculator
Last reviewed 12 September 2026
Tested that the deflator returns exactly 100 when nominal and real output coincide, which is the base-year definition the index rests on.
Inflation Rate Calculator
Last reviewed 12 September 2026
Property-tested that the rate is measured against the starting index rather than reported as a change in index points, which is the error the page exists to prevent.
Purchasing Power Calculator
Last reviewed 12 September 2026
Verified that purchasing power compounds rather than subtracting, and shortened the opening so the tool is reachable without scrolling past an explanation.
Unemployment Rate Calculator
Last reviewed 12 September 2026
Tested that the denominator is the labour force rather than the population, which is what makes the rate fall when discouraged workers stop looking.
Labor Force Participation Rate Calculator
Last reviewed 12 September 2026
Verified that participation is bounded at 100% and that it moves independently of the unemployment rate, which is why the two must be read together.
Debt-to-GDP Ratio Calculator
Last reviewed 12 September 2026
Documented that the ratio compares a stock against a flow, and tested that values above 100% are reported rather than clamped.
Money Multiplier Calculator
Last reviewed 12 September 2026
Verified that the multiplier is the reciprocal of the reserve ratio and that potential money creation scales linearly with the injection.
Velocity of Money Calculator
Last reviewed 12 September 2026
Tested that velocity is nominal output over the money stock, and documented that the figure is uninterpretable without naming which monetary aggregate was used.
Quantity Theory of Money Calculator
Last reviewed 12 September 2026
Verified the MV = PY identity in both directions, so the price level returned always reproduces the nominal output the money side implies.
Sharpe Ratio Calculator
Last reviewed 12 September 2026
Verified that the risk-free rate is subtracted before dividing, since a high return in a high-rate environment is not the same achievement as the same return when cash pays nothing.
Sortino Ratio Calculator
Last reviewed 12 September 2026
Tested that the Sortino ratio exceeds the Sharpe ratio whenever downside deviation is below total volatility, which is the entire reason the measure exists.
Maximum Drawdown Calculator
Last reviewed 12 September 2026
Tested that drawdown is measured from the running peak rather than the opening value, and that the recovery figure always exceeds the drawdown it reverses.
Expected Return Calculator
Last reviewed 12 September 2026
Verified that the expected value always lies between the best and worst scenarios, and that the probability total is reported so weights not summing to 100% are visible.
Holding Period Return Calculator
Last reviewed 12 September 2026
Tested that the capital and income components always reconcile to the total return, so the split cannot drift from the headline figure.
Annualized Return Calculator
Last reviewed 12 September 2026
Verified the compound rate against the growth multiple it implies, and confirmed it never exceeds the total return divided by the years — the error this page exists to correct.
XIRR Calculator
Last reviewed 12 September 2026
Verified that the solved rate discounts every cash flow back to zero at its own date, checked against an independently written present-value function rather than the engine’s own.
Portfolio Return Calculator
Last reviewed 12 September 2026
Tested that the weighted return always falls between the best and worst holding, and that the total weight is reported so weights not summing to 100% are visible.
Effective Tax Rate Calculator
Last reviewed 12 September 2026
Property-tested that the effective rate never exceeds the marginal rate under a progressive table, which is the distinction the page exists to draw.
Taxable Income Calculator
Last reviewed 12 September 2026
Tested that every deduction reduces the taxed figure and that the reported reduction percentage reconciles to the deductions entered.
Payroll Tax Calculator
Last reviewed 12 September 2026
Verified that the employer half is reported separately and added to total employment cost, since it never appears on a payslip.
Tax Refund Calculator
Last reviewed 12 September 2026
Tested that the result flips sign correctly around the break-even point, so a balance owed is reported as owed rather than as a negative refund.
Bonus Tax Calculator
Last reviewed 12 September 2026
Verified both withholding methods against each other, and documented that withholding is not the final tax — the annual return reconciles it.
Overtime Tax Calculator
Last reviewed 12 September 2026
Tested that the overtime rate is the base rate times the multiplier and that tax applies at the marginal rate only, not to regular pay.
Estimated Tax Payment Calculator
Last reviewed 12 September 2026
Verified that existing withholding is subtracted before the quarterly split, so the instalments do not double-count tax already being collected.
Quarterly Tax Calculator
Last reviewed 12 September 2026
Tested that the remaining liability divides across the quarters actually left rather than across four, which is what makes catching up work.
Corporate Tax Calculator
Last reviewed 12 September 2026
Verified that any surcharge raises the effective rate above the headline rate, and that after-tax profit always reconciles to profit less tax.
Dividend Tax Calculator
Last reviewed 12 September 2026
Tested that tax and net income always sum to the dividend, and documented that the applicable rate depends on whether the dividend qualifies.
Loan to Value Calculator
Last reviewed 12 September 2026
Tested both directions — LTV from a loan, and the maximum loan at a target LTV — so the two modes cannot disagree on the same property.
Net Operating Income Calculator
Last reviewed 12 September 2026
Verified that every expense line reduces NOI and that the implied cap rate is NOI over the price, so the two figures cannot drift apart.
Gross Rent Multiplier Calculator
Last reviewed 12 September 2026
Tested that the implied market value is annual rent times the market multiple, and that the value gap reconciles to your own price.
Vacancy Rate Calculator
Last reviewed 12 September 2026
Verified that vacancy and occupancy always sum to 100%, and that lost rent reconciles to the empty days across the unit count.
Rental Yield Calculator
Last reviewed 12 September 2026
Tested that net yield never exceeds gross yield and that the gap is exactly expenses plus vacancy over the price.
Step-Up SIP Calculator
Last reviewed 12 September 2026
Tested that a zero step-up reproduces a flat SIP exactly, and that total invested always reconciles with the contributions actually made.
NPS Calculator
Last reviewed 12 September 2026
Tested that the lump sum and annuity corpus always add back to the full corpus, and that a 100% annuity share leaves no lump sum.
Loan Affordability Calculator
Last reviewed 12 September 2026
Tested that a longer tenure always raises the maximum loan and the total interest together, and that a zero rate makes the loan the payments summed.
Overtime Pay Calculator
Last reviewed 12 September 2026
Tested that zero overtime hours leaves only regular pay, and that a multiplier of one makes overtime hours worth exactly the base rate.
Cost of Living Calculator
Last reviewed 12 September 2026
Tested that the percentage change and the absolute difference always agree with the required salary the ratio produces.
Indexation Calculator
Last reviewed 12 September 2026
Tested that an unchanged index leaves the cost untouched, and that indexation can never increase the taxable gain.
Average Cost Basis Calculator
Last reviewed 12 September 2026
Tested that the weighted average always falls between the cheapest and dearest lot price, and equals it when only one lot has units.
Economic Order Quantity Calculator
Last reviewed 12 September 2026
Tested that ordering cost and holding cost are equal at the optimum, which is the defining property of the EOQ solution.
Kruskal-Wallis Calculator
Last reviewed 9 September 2026
Reports a negative epsilon-squared rather than clamping it. It is (H - k + 1)/(n - k), which goes below zero when H falls short of its null expectation — the groups separating less than chance would produce, which is a finding rather than an error.
Wilcoxon Signed-Rank Calculator
Last reviewed 9 September 2026
Warns when the differences are too asymmetric for a median reading. The test asks whether the differences are centred at zero, and that becomes a claim about the median difference only under symmetry — the same gap that makes Mann-Whitney not a median test.
APY Calculator
Last reviewed 9 September 2026
Verified the effective-rate conversion against an independent expm1/log1p computation and property-tested that the yield rises with compounding frequency and never exceeds the continuous limit.
Balance Transfer Calculator
Last reviewed 9 September 2026
Documented and tested the no-paydown simplification behind the avoided-interest figure, and confirmed the break-even point depends only on the fee percentage and the rate, not on the balance size.
Bond Yield Calculator
Last reviewed 9 September 2026
Replaced the textbook approximate yield to maturity with an exact solve by bisection, after testing showed the shortcut could understate the yield by more than 20 percentage points on a short, deeply discounted bond and could even print a yield below the current yield, which a true YTM on a discount bond never does. The shortcut is now shown as a separate, labelled line so its error is visible, and the worked example, methodology and FAQ were corrected — they had previously claimed the exact yield would be lower than the approximation when it is higher.
Cap Rate Calculator
Last reviewed 9 September 2026
Surfaced the implied valuation at an 8% cap rate, which the page had been calculating but never displaying, so the effect of a shift in market cap rates is now visible alongside the 6% figure.
Capital Gains Tax Calculator
Last reviewed 9 September 2026
Corrected the short-term rate, which had been read from the single-filer bracket table for every filing status — taxing a joint filer on 75,000 dollars of income at 22% instead of 12%. Ordinary-income brackets now come from the same sourced federal table the Income Tax Calculator uses.
Car Depreciation Calculator
Last reviewed 9 September 2026
Property-tested that the percentage of value lost depends only on the rate and the age, which is what makes the figure comparable between cars of different prices.
Closing Cost Calculator
Last reviewed 9 September 2026
Fixed a breakdown that did not add up: the total already included the appraisal, prepaid interest and escrow setup, but only the origination, title and government lines were shown, so the itemisation on screen could not be reconciled against the headline figure. Every component is now displayed.
Credit Utilization Calculator
Last reviewed 9 September 2026
Confirmed that an over-limit balance reports above 100% rather than clamping, since hiding that is the opposite of what someone checking utilisation needs.
Debt-to-Income Ratio Calculator
Last reviewed 9 September 2026
Property-tested that the gap between the front-end and back-end ratios is exactly non-housing debt over income.
Dividend Yield Calculator
Last reviewed 9 September 2026
Property-tested that the income split stays exact and that yield on cost exceeds current yield precisely when the shares have appreciated.
Emergency Fund Calculator
Last reviewed 9 September 2026
Property-tested that the months-to-goal figure always closes the shortfall and never overshoots by a whole extra month.
Extra Mortgage Payment Calculator
Last reviewed 9 September 2026
Fixed an off-by-one in the shortened-term solve that reported minus one month saved when no extra payment was entered, and confirmed by simulation that the solved payoff month is the first one that actually clears the balance.
FIRE Calculator
Last reviewed 9 September 2026
Surfaced the exact month count behind the rounded years figure, which the page had been calculating but not displaying, and checked the accumulation loop against a closed-form solve.
HELOC Payment Calculator
Last reviewed 9 September 2026
Confirmed by simulation that draw-period payments leave the balance exactly unchanged, which is what makes the step-up to the repayment payment the number worth showing.
Home Equity Loan Calculator
Last reviewed 9 September 2026
Property-tested that borrowing the stated maximum lands exactly on the 85% combined loan-to-value cap the page quotes.
Rental Property Calculator
Last reviewed 9 September 2026
Cross-checked the cap rate against the standalone Cap Rate Calculator on the same building, and confirmed the cap rate stays unlevered while cash-on-cash responds to the financing.
Self-Employment Tax Calculator
Last reviewed 9 September 2026
Corrected the deductible half of the self-employment tax, which had been including the 0.9% Additional Medicare Tax. That surtax is reported on Form 8959 and is not part of the one-half-of-SE-tax deduction, so the deduction was overstated for higher earners.
Student Loan Calculator
Last reviewed 9 September 2026
Verified the payment by simulating the loan month by month to a zero balance, rather than only re-running the amortisation formula.
Cash Conversion Cycle Calculator
Last reviewed 8 September 2026
Treats a negative cycle as a business model rather than an input error, and says why: below zero, customers pay before suppliers do, so the supply chain funds growth instead of capital. The page also records the failure mode that comes with it, which is that the mechanism reverses when sales stop growing.
DSO Calculator
Last reviewed 8 September 2026
States plainly that DSO is not "how long customers take to pay" but a stock over a flow, so it rises with growth even when every customer pays on the identical day of identical terms — the single most common way a receivables metric misleads the people reading it.
DIO Calculator
Last reviewed 8 September 2026
Records that FIFO and LIFO produce genuinely different DIO for identical warehouses when prices are rising, so a cross-company comparison is only valid once the cost-flow assumption in the accounting-policy note has been checked.
DPO Calculator
Last reviewed 8 September 2026
Documents where the familiar textbook figure of 36.7% comes from — it is the 360-day convention, against 37.2% simple and 44.6% compounded on 365 days — and the validator asserts all three rather than repeating the claim.
Current Ratio Calculator
Last reviewed 8 September 2026
Also retires the "2.0 is healthy" rule of thumb explicitly: it is a mid-century manufacturing heuristic, and supermarkets run below 1 permanently without distress because their stock sells for cash before supplier invoices fall due.
Quick Ratio Calculator
Last reviewed 8 September 2026
States the limit the acid test is usually credited with not having: it removes inventory but keeps receivables, so a comfortable quick ratio on a ledger collecting in 90 days is a promise rather than liquidity. The page routes that question to the DSO calculator instead of hand-waving it.
Cash Ratio Calculator
Last reviewed 8 September 2026
The three rungs are computed by three separate engine functions rather than derived from one another, and the ordering current >= quick >= cash is then asserted as a property over five thousand generated balance sheets — an ordering that fell out of shared code by accident would still look right while a function was wrong.
Working Capital Calculator
Last reviewed 8 September 2026
Treats negative working capital as a funding model rather than a defect — customers paying before suppliers is how grocers and marketplaces finance growth — while recording the specific risk that the mechanism reverses when volume stops growing and payables still fall due.
Debt to Equity Calculator
Last reviewed 8 September 2026
Carries a lease toggle showing what the same company looked like before IFRS 16 put lease liabilities on the balance sheet in 2019 — retailers and airlines saw gearing jump overnight with no change in the business, so any trend line crossing that date needs both sides restated.
Interest Coverage Ratio Calculator
Last reviewed 8 September 2026
Documents the interest the denominator does not contain: under IAS 23, borrowing costs on qualifying assets are capitalised into the asset rather than expensed, so a business mid-construction reports better cover than its cash position warrants. Also reports negative cover for a loss-making company as a real result rather than as no data.
Altman Z-Score Calculator
Last reviewed 8 September 2026
Prints each term’s ratio, coefficient and contribution, and explains why retained earnings dominates: X2 is cumulative, so a young and profitable company scores badly for reasons unrelated to distress. The model was fitted on mature listed manufacturers and the page is explicit about where that stops applying.
Expected Value Calculator
Last reviewed 8 September 2026
Reports probabilities that do not sum to 1 rather than normalising them silently, since a set summing to 1.4 is a missing or double-counted outcome and rescaling would conceal it. Also fixed a preset whose label said 'positive expected value' while computing −0.33.
Monty Hall Calculator
Last reviewed 8 September 2026
The simulation alongside is seeded, so the figure quoted on the page is the figure a reader sees. It exists because this is the one probability result that algebra reliably fails to settle and observed frequencies reliably do — Erdős himself refused the algebra and accepted the simulation.
Birthday Paradox Calculator
Last reviewed 8 September 2026
Exposes the day count as an input, because the same square-root law governs hash collisions: a space of a million values starts colliding at about 1,178 items, and a 32-bit identifier at about 77,000 records.
Simpson's Paradox Calculator
Last reviewed 8 September 2026
Corrected a claim in an earlier draft. I had written that a reversal is impossible when either the base-rate spread or the composition spread is zero; only the first half holds. With identical composition the pooled difference is a positively-weighted average of the stratum differences, so it cannot overturn a unanimous verdict, but a bare majority can still be outweighed by one large stratum. Both directions are now asserted over a thousand generated datasets.
Mann-Whitney U Calculator
Last reviewed 8 September 2026
Reports the probability of superiority and the rank-biserial correlation as the effect size, since U itself scales with both sample sizes and is not comparable across studies.
One-Way ANOVA Calculator
Last reviewed 8 September 2026
Reports omega squared beside eta squared, since eta squared includes the between-group variation that arises by chance and always overstates the effect.
Odds Ratio Calculator
Last reviewed 8 September 2026
Shows the absolute risk difference and the number needed to treat alongside, since a relative figure with no baseline describes a move from 40% to 80% and one from 0.001% to 0.002% equally well.
Effect Size Calculator
Last reviewed 8 September 2026
Applies the exact Hedges correction rather than the square-root approximation, and states that Cohen's 0.2, 0.5 and 0.8 benchmarks were explicitly provisional rather than derived.
Coefficient of Determination Calculator
Last reviewed 8 September 2026
Reports negative R-squared rather than clamping it to zero, since an out-of-sample value below zero is the clearest signal that a model has fitted noise.
Probability Calculator
Last reviewed 8 September 2026
Refuses probabilities that describe no possible world — P(A) = 0.8 with P(B) = 0.7 and an overlap of 0.1 breaks the Frechet bounds, and most calculators return an answer anyway.
Kurtosis Calculator
Last reviewed 8 September 2026
Warns when a single observation supplies more than 40% of the fourth moment, since the kurtosis is then a statement about that point rather than about the distribution.
Skewness Calculator
Last reviewed 8 September 2026
Includes a six-value counterexample to the mean-median rule taught almost universally: 7, 3, 11, 11, 18, 9 has a moment skewness of +0.361 with a mean of 9.833 sitting below its median of 10.
Covariance Calculator
Last reviewed 8 September 2026
Demonstrates that zero covariance is not independence: with x symmetric about zero and y equal to x squared, y is completely determined by x and the covariance is exactly zero.
Outlier Calculator
Last reviewed 8 September 2026
Shows all eleven quartile conventions, because the IQR fence depends on which one you use. On the values 1 to 9 plus 15, exactly one of the eleven flags the 15 — type 7, the default in R, NumPy and Excel.
Correlation Coefficient Calculator
Last reviewed 8 September 2026
Uses midranks for Spearman, so it stays correct under ties where the familiar six-sigma-d-squared shortcut is silently wrong — on one small example the shortcut returns 0.2321 against a correct 0.1989.
Empirical Rule Calculator
Last reviewed 8 September 2026
Uses the survival function for the one-tail figure rather than one minus the CDF, so the number stays accurate past six sigma where the subtraction would lose every significant digit.
Central Limit Theorem Calculator
Last reviewed 8 September 2026
At n = 2 the coverage still reads 95.11% while the lower tail is identically zero, because the interval reaches below a value the population can never produce. Judged on coverage this population passes at n = 2; judged on its tails it needs n = 135.
Beta Distribution Calculator
Last reviewed 8 September 2026
Inverts the CDF by bisection rather than Newton's method, because the density is unbounded at an endpoint whenever a parameter falls below 1 and the derivative Newton divides by runs to infinity there.
Negative Binomial Calculator
Last reviewed 8 September 2026
Prints the variance divided by the mean, which is 1/p identically — the reason overdispersed count data gets modelled with this distribution instead of a Poisson.
Uniform Distribution Calculator
Last reviewed 8 September 2026
Explains why the continuous form makes the strict and non-strict inequalities identical, which is a real distinction in the discrete form and no distinction at all in the continuous one.
Lognormal Distribution Calculator
Last reviewed 8 September 2026
Reports the share of the population below its own arithmetic mean — 65.54% at the default parameters — because that single figure is why median income and mean income tell different stories.
Weibull Distribution Calculator
Last reviewed 8 September 2026
Corrects the common misreading of the scale parameter: lambda is the characteristic life, the 63.2nd percentile at every shape, and it equals the mean only when k is 1.