Every formula behind a MathCalcTools calculator, in one table, each with a worked example. Updated July 2, 2026.
MathCalcTools runs 17 calculators, and each one uses a single standard, named formula: for example the square root tool uses sqrt(n) = x, where x * x = n, and the quadratic solver uses the quadratic formula, x = (-b ± sqrt(b^2-4ac)) / 2a. The full table below lists the formula and one worked example for every tool on the site, and the same table is available as a CSV.
| Calculator | Formula | Worked example | Result |
|---|---|---|---|
| Square Root | sqrt(n) = x, x⋅x = n | sqrt(72) | 6√2 ≈ 8.485 |
| Quadratic Formula | x=(-b±√(b²-4ac))/2a | x²-5x+6=0 | x = 2, 3 |
| Slope of a Line | m=(y2-y1)/(x2-x1) | (1,2) to (4,11) | m = 3 |
| Derivative (power rule) | d/dx[x^n]=n⋅x^(n-1) | d/dx[x³] | 3x² |
| Integral (power rule) | ∫x^n dx = x^(n+1)/(n+1)+C | ∫x² dx | x³/3 + C |
| Exponent | a^n = a×a×...×a | 2^5 | 32 |
| Factoring (quadratic) | x²+bx+c=(x+p)(x+q) | x²+7x+12 | (x+3)(x+4) |
| GCF | largest common factor | GCF(24, 36) | 12 |
| Pythagorean Theorem | a²+b²=c² | legs 3, 4 | hyp = 5 |
| Standard Deviation | σ=√(Σ(x-μ)²/n) | {2,4,4,4,5,5,7,9} | σ ≈ 2.0 |
| Average (mean) | mean = Σx / n | {4, 8, 15} | mean = 9 |
| Rounding | round to place value | 3.14159, 2 dp | 3.14 |
| Volume (cylinder) | V = πr²h | r=3, h=10 | V ≈ 282.7 |
| Square Footage | area = l × w | 12ft × 15ft | 180 sq ft |
| Ohm's Law | V = I × R | I=2A, R=5Ω | V = 10V |
| Right Triangle | sinθ=opp/hyp | 30-60-90, hyp=10 | sides 5, 5√3 |
| Triangle Area (Heron's) | √(s(s-a)(s-b)(s-c)) | sides 5, 6, 7 | Area ≈ 14.70 |
Every row uses the exact formula implemented in that calculator's own code on this site, so the table stays consistent with what the live tools compute. These are standard, named mathematical formulas (the quadratic formula, the power rule, Heron's formula, and so on) rather than statistics that need an external source, so no outside citation is required for accuracy. Worked examples were run through each live calculator to confirm the result shown here matches the tool. This page is reviewed whenever a calculator's formula or rounding behavior changes; the "updated" date above reflects the last such review.
Click a calculator name to open the live tool and run your own numbers, or use the table as a quick lookup when you already know the formula and just need to check it. The CSV download carries the same 17 rows if you want to reuse the table in a spreadsheet or cite a specific formula elsewhere.
Jessica Martinez spent six years reading loan disclosures and expense reports for a living before she started writing about numbers instead of just checking them. On MathCalcTools she keeps every worked example honest: the same steps a calculator runs, written out so a reader can follow along, not just copy an answer.