Convexity Calculator
The formula
What the convexity tells you
The bottom line for convexity and the margin it represents — the two numbers every owner checks before anything else.
Calculation: profit = revenue − costs; margin = profit ÷ revenue. Enter your inputs and every substitution is shown below the result.
Reading the result
A positive result with a sub-5 % margin is fragile; read the margin band, not just the sign.
Limitations and best practice
Accrual vs cash: this is P&L arithmetic — a profitable business still fails without the cash to pay Friday.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is margin the whole story?
Which costs count?
Source & methodology
Standard income-statement arithmetic.
How Convexity works — and what your result really means
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on a Convexity page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
The useful way to hold Convexity is as a ratio with a story attached: profit = revenue − costs; margin = profit ÷ revenue says how the parts combine, and the $-46,000.00 figure above is simply that sentence written in numbers. Everything that follows unpacks one clause of the sentence at a time.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. Convexity translates that bet: profit = revenue − costs; margin = profit ÷ revenue. The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
Nothing below is stock text pasted around a number: the worked example computes net profit = $-46,000.00 from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Total costs first, at ≈25.0 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
Inside the Convexity calculation: formula and every input
The engine implements a single stated model: profit = revenue − costs; margin = profit ÷ revenue. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Revenue / gross value ($) (example value 69,000) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Total costs ($) (example value 115,000) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Periods to compare per-month figures (example value 16) is a measured number in the unit named by the label; the formula does not convert for you. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
A fully worked Convexity example
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Revenue / gross value ($), Total costs ($), Periods to compare per-month figures. The endpoint of that chain is $-46,000.00 of net profit, sitting in the “Loss at these figures — the cost base is the problem” band.
- Profit = $69,000.00 − $115,000.00 = $-46,000.00
- Margin = ÷ revenue = -66.7 %
Margin — -66.7%. This is the number experienced users quote when the headline alone would mislead.
Cost coverage ratio — 0.60 ×. Compare it against the main result of $-46,000.00 before drawing conclusions.
Per period — $-2,875.00. Compare it against the main result of $-46,000.00 before drawing conclusions.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Convexity at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Convexity was recomputed at 5 points along the dominant input, with every other field left untouched.
| Total costs setting | Net profit |
|---|---|
| 80 % of the example value | $-23,000.00 |
| 90 % of the example value | $-34,500.00 |
| example inputs | $-46,000.00 |
| 110 % of the example value | $-57,500.00 |
| 120 % of the example value | $-69,000.00 |
The corridor runs from $-69,000.00 to $-23,000.00 across that band — which is the range worth planning inside rather than the single $-46,000.00 point estimate. Reproduce it in the form above by editing Total costs alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Convexity the most
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the net profit recomputed, so the ranking below is measured rather than asserted. For Convexity the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Total costs: ten percent up gives $-57,500.00, ten percent down gives $-34,500.00 — ≈25.0 % of the net profit either way
- Nudge Revenue / gross value by ±10 % and Convexity lands between $-52,900.00 and $-39,100.00 (sensitivity ≈15.0 %)
Total costs is the dominant lever here: ten percent either way moves the result by about 25.0 %, from $-57,500.00 to $-34,500.00. Measure that input from a document rather than from memory, and treat Revenue / gross value as the second priority (≈15.0 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Is your Convexity good — reading the result bands
Nobody acts on a bare figure — they act on a figure with a comparison attached. The verdict attached to the default calculation — “Loss at these figures — the cost base is the problem” — is one band on a ladder your own figure may sit somewhere else on. How much of that band is luck? On Total costs alone ten percent either way covers $-57,500.00 to $-34,500.00. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Related measures answer related questions, and the distinctions matter: Convexity is the quantity, Net profit is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Common mistakes with Convexity (and the fix)
Accrual vs cash: this is P&L arithmetic — a profitable business still fails without the cash to pay Friday. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Chasing one metric. Convexity needs its pair (Margin) the way a speedometer needs fuel pressure — one number alone has burned more portfolios than bad markets.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Total costs dominating — a careful figure there beats false precision everywhere else.
The subtlest error is answering the wrong question precisely. Confirm that net profit is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Convexity verification checklist
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Put Total costs under a magnifier; the sensitivity table above is the reason why.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Note the date and the inputs beside the number so the figure can be audited later.
- Confirm the answer against one independent method or published benchmark for Convexity.
Step by step: getting a trustworthy Convexity out of this tool
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — gather before you type. Convexity depends on revenue / gross value ($), total costs ($), periods to compare per-month figures. Collect them from a source document — a statement, a report, an invoice, a log — rather than from memory, because recalled inputs are the single largest cause of wrong results. The test of a good estimate is not that it feels right but that it changes what you do.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. Note the assumption you are least sure about; that is where the real risk lives.
Step 3 — measure what deserves measuring. The ranked levers above tell you where a careful figure pays off. Everything else can stay approximate, which is a licence to stop hunting for data you do not need. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 5 — schedule the next run. In Investing & Markets the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Where Convexity matters in practice
Investing & Markets arguments end at arithmetic or they do not end. Convexity is the arithmetic: $-46,000.00 on the example inputs, reproducible by anyone who types the same numbers. A result worth acting on survives having its two shakiest inputs halved.
Professionals in Fixed Income use this style of calculation as a screening filter before spending real money or effort: a quick Convexity check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Treat Convexity like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. One decimal place more than your data supports is one decimal place of fiction.
The questions that come up most about Convexity
What affects Convexity the most?
Measured on this engine, Total costs is the dominant lever: moving it ±10 % shifts the net profit across $-57,500.00 to $-34,500.00 — about 25.0 % of the headline, with Revenue / gross value next at ≈15.0 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: revenue / gross value or total costs?
For Convexity, Total costs wins the head-to-head (≈25.0 % against ≈15.0 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Convexity?
There is no honest universal average for Convexity, but there is a reference point: the defaults on this page produce $-46,000.00 (Loss at these figures — the cost base is the problem). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Convexity by hand?
Use the stated model — profit = revenue − costs; margin = profit ÷ revenue — and substitute in the order the tool prints (it starts from Profit = $69,000.00 − $115,000.00 = $-46,000.00). On the example inputs the hand route lands on $-46,000.00, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Convexity if total costs changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the net profit goes across $-57,500.00 to $-34,500.00, a swing of roughly 25.0 % around the $-46,000.00 baseline. That ratio is the practical definition of how much this input matters.
Is the Convexity result of $-46,000.00 good or bad?
Neither, on its own — the label “Loss at these figures — the cost base is the problem” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Total costs alone moves it by ≈25.0 %.
How often should I check Convexity?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Convexity is a snapshot, not a subscription; stale snapshots are the most common silent error in Investing & Markets planning.
Is Convexity accurate?
The arithmetic is exact: profit = revenue − costs; margin = profit ÷ revenue is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the $-46,000.00 result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Is margin the whole story?
No — capital turnover decides ROE. A 5 % margin at 10× turnover beats a 30 % margin at 0.5×.
Which costs count?
Everything below the definition you chose. State gross or net, and keep the same definition across periods.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Glossary for Convexity
- Margin
- -66.7% on the example inputs — a companion figure printed beside the headline of Convexity so that no result is read in isolation.
- Cost coverage ratio
- 0.60 × on the example inputs — a companion figure printed beside the headline of Convexity so that no result is read in isolation.
- Per period
- $-2,875.00 in the default Convexity calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Net profit
- The primary output of this tool: $-46,000.00 for the default inputs, computed exactly from profit = revenue − costs; margin = profit ÷ revenue.
- Worked example
- The calculation written out in full so that nothing on this page has to be taken on trust.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Loss at these figures — the cost base is the problem”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Convexity moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
There is no black box on this page — the engine evaluates profit = revenue − costs; margin = profit ÷ revenue. Source of record: Standard income-statement arithmetic. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
What to do with your Convexity next
Save the number together with its inputs and today’s date; a Convexity figure without context is unusable the moment an input changes.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.