Sumvia

Business Math Calculators

Sumvia is a small publication about the arithmetic of running a business — margins, markup, break-even points, returns, growth rates, tax, commission, and pay. Each topic gets one focused calculator page: the formula, an interactive tool, and worked examples that are generated at build time by the same tested code that powers the tool, so the explanation can never drift from the calculation. Everything runs in your browser; nothing you type is sent to a server.

Pricing and margins

What to charge, what you keep, and what a change in price really does.

  • Profit Margin — gross margin from cost and price, with the equivalent markup alongside
  • Markup — set a selling price from cost and a target markup
  • Profit — net profit and margin from revenue and total costs
  • Price Change — the true percentage behind a rise, a drop, or a rollback
  • Discount — sale prices, stacked discounts, and what the seller gives up
  • Unit Price — compare pack sizes on cost per unit instead of shelf price
  • VAT — add or strip value-added tax at any rate, both directions

Returns and growth

Whether a spend paid off, and how fast something actually grew.

  • ROI — return on investment, with the annualized rate when you give it a duration
  • CAGR — compound annual growth rate — the honest average over multiple years
  • Break-Even — the units or revenue where a product stops losing money
  • SaaS Metrics — LTV, LTV:CAC, payback months, and honest annual churn from four inputs
  • Simple Interest — I = P·r·t for loans and deposits that do not compound

Pay and sales

What a sale pays, what a job pays, and what the hours add up to.

  • Commission — flat and tiered commission on a sale or a period of sales
  • Salary — convert between hourly, weekly, monthly, and annual pay
  • Overtime — regular and overtime earnings at 1.5×, 2×, or a custom multiplier
  • Time Card — weekly hours from clock-in and clock-out times, breaks deducted

The confusion these pages exist to prevent

Most business-math mistakes are not arithmetic slips — they are the right formula applied to the wrong base. The two most expensive examples, with the numbers computed by our engine:

Margin is not markup. Buy at 60 and sell at 100 and you have made 40 of profit — but that one sale is a 66.67% markup (profit over cost) and only a 40% margin (profit over price). Quote a supplier the wrong one and you misprice by a wide margin, literally. The profit margin calculator always shows both percentages side by side so the two cannot be confused.

Average growth is not compound growth. A value that doubles in five years grew 100% in total, which feels like 20% a year — but the honest compound rate is 14.87% per year, because each year grows on top of the last. Dividing total growth by the number of years overstates every multi-year trend you will ever quote. The CAGR calculator computes the compound rate and shows the gap.

How every page here is built

Each calculation engine is a small, typed function with automated tests over standard inputs, decimals, negatives, zeros, and edge cases. The worked examples in the prose and FAQs are computed by that same engine when the site is built — a wrong figure fails the build rather than getting published. The full discipline is documented on the methodology page, and about Sumvia explains who is behind it. Results here are aids, not advice: verify anything consequential before you act on it.

Beyond the business cluster

Sumvia is also the studio behind a small network of single-purpose sites, each doing one job on its own domain: