How PhDino checks its numbers

Maintained by Andrea Coppola · Last reviewed 21 September 2026

A calculator is only worth using if its numbers are right. This page explains where the formulas come from, how each calculator is tested, what those tests can and cannot prove, and lists every error found and corrected so far.

Test coverage of the current build. 97 calculators are covered by 184 test cases making 564 value checks. 85 have at least one reference case worked out independently of the calculator; the other 12 are documented rules of thumb whose behaviour the tests pin. These figures are written by the test suite itself each time the site is built.

Where the formulas come from

The calculators implement standard, published engineering, physics, chemistry and clinical relationships: Euler–Bernoulli beam theory, Euler and AISC column buckling, Manning's equation, Ohm's law, the Tsiolkovsky rocket equation, Mifflin–St Jeor and Cockcroft–Gault, and so on. Where a design standard or code stands behind a calculator (AISC 360, ACI 318, the NEC, ASTM, ASHRAE) the standard is named on the page, but its tables and text are not reproduced. To design to a code you need the current official edition.

Some calculators are rules of thumb rather than derived physics: an asphalt thickness estimate, an HVAC load per square foot, a maximum heart rate of 220 minus age. These are labelled as such, and the tests pin their documented behaviour so it cannot change unnoticed.

How every calculator is tested

Each time the site is built, an automated suite runs every calculator and compares its outputs with expected values. The expected values are not produced by the calculator's own code. They are worked out another way: through SI units where the calculator uses US units, from closed-form expressions written out again, or from published constants and tables such as standard-atmosphere density, orbital parameters, bearing capacity factors and the speed of sound. A unit slip of the kind that once made a 20 ft beam deflect 730 inches fails the build instead of reaching a visitor.

The suite also checks the wiring: that every input actually changes some output, that a calculator's declared outputs are the ones it returns, that a recipe only passes values into fields that exist, and that every calculator has a written guide.

Worked examples in the guides

24 calculator guides and all 11 project guides include a worked example. The numbers in the text are not typed in: each one is filled in from a real run of the calculator with the example's inputs, so the text cannot drift away from the calculator, and the build fails if a number cannot be resolved. The project guides chain several calculators, and each step's inputs are built from the earlier steps' results in the same way.

The build also checks that each example's key outputs match values that were worked out separately, in SI units, by a closed-form expression or from published constants. Where a guide adds a hand check next to a calculator's output, for example the sliding check in the retaining-wall guide or the plane-change burn in the orbital guide, that figure is computed from the formula named in the text. Those extras are not covered by the reference tests, and the guide says when a figure comes from a hand check.

What the tests do not prove

The tests were written by the site's maintainer with AI assistance. They show that a calculator computes the formula it claims to compute, correctly and consistently. They do not show that a formula is appropriate for your situation, that a simplification is acceptable for your design, or that a licensed engineer (or, for the biomedical calculators, a clinician) has reviewed the site. Treat results as an educational estimate and check anything that matters against the governing standard or a qualified professional.

Simplifications are stated, not hidden

When a calculator omits something that could mislead, for example cable sizing that checks voltage drop but not ampacity, or a truss check that ignores buckling in compression, a "Limits" notice appears at the top of its page and its window. The guide then explains what is left out and what to use instead.

Units

Every calculator works in one set of units internally, and converts what you type to those units and its results back to yours. You can switch between imperial and metric, or change the unit of a single field. The conversions are part of the tested behaviour.

Biomedical calculators

The biomedical calculators (BMI, body surface area, creatinine clearance, IV drip rate and others) use standard published formulas and carry a prominent warning that they are for education only. The two that involve medication doses, weight-based dosing and pediatric dosing, are excluded from search engines and kept only for use inside the app. Never use any result to decide on treatment.

Review dates and corrections

Each guide shows the date it was last reviewed. The whole set was last reviewed on 21 September 2026. If you find an error, please report it through the Contact page: verified errors are fixed, dated and listed below, with the numbers that were wrong and the numbers that are right.

Corrections log

Errors that were found and fixed, newest first. Each entry gives the wrong behaviour in numbers and the correct one.

2026-09-21 — Worked-example tables (two values rounded). In the "You enter" tables of two project guides a typed value was shown rounded to four significant figures, contradicting the text beside it: the Plan an Orbital Maneuver guide showed a 35,786 km orbit altitude as 35,790 km, and the Prepare a Lab Solution guide showed a 249.68 g/mol molar mass as 249.7. Only the display was wrong; the calculations used the right values. Fixed, and the build now fails if a typed input is displayed differently from the value that was used.
2026-09-21 — Power Calculation. The formula was always the three-phase one (√3 × V × I × power factor), so a single-phase load showed 73% too much power: a 60 A, 240 V load at a power factor of 0.9 read 22.45 kW instead of 12.96 kW. A System selector (three-phase or single-phase) was added. The Size a Home Backup Generator guide, which is about a single-phase house, was rebuilt around it and now starts from running and starting watts.
2026-09-21 — Design a Synchronous Circuit's Timing (guide). The guide fed the same path delay into the setup and the hold check and started the clock period at the bare gate delay. Setup is decided by the longest path and hold by the shortest, and the period must also cover the clock-to-Q delay and the setup time: for the 12-gate example the true minimum period is 3.55 ns, not 3.00 ns, so the gate delay alone overstated the achievable frequency by 18%. The guide now runs the check twice.
2026-09-21 — Machine a Part from Raw Stock (guide). The guide passed a milling cutter's spindle speed into the drilling estimate, but a drill's diameter and cutting speed give a different RPM (a 1/2 in cutter at 350 SFM turns 2,674 RPM, a 1/4 in drill at 200 SFM turns 3,056 RPM). The speeds calculation is now run for the drill itself, with two flutes and a chip load per tooth, so its feed rate agrees with the cycle-time estimate.
2026-09-21 — Beam Deflection. The results were wrong for every input. The load was used in lb/ft where the formula needs lb/in, and Young's modulus in ksi where it needs psi, so deflection came out 12,000 times too large (730 in for the 20 ft example instead of 0.061 in) and bending moments 12 times too large. The article also gave the cantilever moment as wL/2; the correct value is wL²/2. Fixed, and a span-to-deflection ratio was added.
2026-09-21 — Column Buckling. The "critical load" was actually a stress (345 ksi for the example, above the yield strength of steel), shown as a load, and the calculator had no cross-section area. Rebuilt on the AISC 360 column curve with area and yield strength as inputs; it now reports critical stress, nominal capacity and design capacity. The Build a Deck guide had told readers to copy this capacity into Footing Design as the load on each footing. That was wrong, because a column's capacity is not the load it carries, and the guide now works the load out from the area each post supports.
2026-09-21 — Shaft Torsion. The angle of twist was 1,000 times too large because the shear modulus was entered in ksi but used as psi (609° instead of 0.61° for the example).
2026-09-21 — Pile Capacity. Capacities were 144 times too large (an area in square inches multiplied by a pressure in pounds per square foot). The calculator now takes unit skin friction and unit end bearing as inputs, as its article always described, and reports an allowable capacity. A "pile type" input that changed nothing was removed.
2026-09-21 — Continuous Beam Moments. Support and span moments were wrong (8 times too large for the 20 ft example) because of mixed units and a shortcut for the support moment that is not exact. Replaced with the exact three-moment result for two spans.
2026-09-21 — Press Brake Tonnage. Tonnage was 60 times too large: the material's tensile strength was multiplied into a chart constant that already contains it. Now 8.98 tons per foot for the 1/8 in mild-steel example, scaled by tensile strength for other materials.
2026-09-21 — Soil Bearing Capacity. All three bearing capacity factors were wrong (for a 30° friction angle Nc was 3.97 instead of 30.14), so the ultimate capacity came out at about a third of the correct value, and a "Settlement 0.5 in" result was a fixed number unrelated to the inputs. Corrected; the settlement figure was removed, and soil unit weight became an input.
2026-09-21 — HVAC Cooling. The airflow figure was about twice what a cooling load needs (roughly 800 CFM per ton). It now uses the sensible-heat equation with a 20°F air temperature difference and the usual assumption that about three quarters of the load is sensible heat, about 417 CFM per ton. (A first correction on the same day gave about 556 CFM per ton because it ignored the latent share; that is fixed too.)
2026-09-21 — Motor Sizing. The required power was divided by the motor's own efficiency, which does not change the rating a motor needs; the efficiency now describes the drive (belts, gears, couplings). Ratings now round up to standard motor sizes, and an invented cost figure was removed.
2026-09-21 — Transformer Sizing. The rating was divided by efficiency and the secondary current overstated by about 4%. It now returns the next standard rating and the correct full-load currents.
2026-09-21 — Footing Design. A 1.4 "load factor" was applied to a service load when sizing against an allowable soil pressure, and two inputs (concrete strength, steel grade) did nothing. The plan size now uses the service load plus a stated self-weight allowance, and the dead inputs were removed.
2026-09-21 — pH Calculator. Water's own ions were ignored, so a very dilute strong acid (10⁻¹⁰ M) showed a pH of 10, which is impossible for an acid. The calculation is now exact.
2026-09-21 — Bit Width & Parity. The parity output was labelled odd parity but is the even-parity bit. The label and the article were corrected.
2026-09-21 — Inputs that did nothing, and solvers that accepted contradictions. The retaining-wall calculator ignored its soil-bearing input and the compaction check ignored its required-compaction input; both were fixed, and a recipe that passed a value into an ignored input was corrected. The Ohm's Law, Ideal Gas Law and Rocket Equation calculators now say which field is solved for (a field left at 0) and refuse four contradictory values instead of quietly showing them.
2026-09-21 — "Limits" notices. Calculators that are simplifications now say so at the top of their page and window: cable sizing checks voltage drop only and not ampacity, truss analysis ignores buckling in compression, wind turbine output assumes a constant wind speed, and the footing, retaining wall, soil bearing, pile and asphalt calculators list what they leave out.

Educational tool — not a substitute for a licensed engineer or the official code text.