Convexity Calculator
The formula
What the convexity tells you
The blend for convexity: weighted mean with the weights shown explicitly, so nobody has to guess whether line one counted.
Calculation: weighted average = Σ(value × weight) ÷ Σ weights. Enter your inputs and every substitution is shown below the result.
Reading the result
Compare with the simple-mean line; a gap means the weighting is doing real work — decide if that is intended.
Limitations and best practice
Weights must share one unit (dollars, hours, kg); mixing units produces a number that is meaningless but still displays fine.
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
When does weighted beat simple?
Can weights be percentages?
Source & methodology
Weighted mean definition.
Convexity explained: formula, worked example and honest limits
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Convexity is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Convexity in real time, and see every substitution printed below.
Banking arithmetic has a second subtlety: fees and rounding that hide in the denominator. The formula above — weighted average = Σ(value × weight) ÷ Σ weights — is the clean version; real products add layers. The habit that protects you is asking "per what, per when?" of every rate you see, and this tool’s companion outputs flag exactly those conversions.
In Finance & Banking the same quantity is often quoted under two or three different conventions. The formula printed above fixes one convention and applies it consistently, which is what makes results from this page comparable with each other.
Nothing below is stock text pasted around a number: the worked example computes convexity = 113.75 from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Third value (use twice for 2-item blends) first, at ≈4.0 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Inside the Convexity calculation: formula and every input
The engine implements a single stated model: weighted average = Σ(value × weight) ÷ Σ weights. 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.
First value (example value 80) is a quantity rather than a category — precision here is cheap and worth having. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Second value (example value 115) 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.
Third value (use twice for 2-item blends) (example value 180) is a quantity rather than a category — precision here is cheap and worth having. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Weight of first (example value 2) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the same conditions each time (same scale, same time of day) so that changes in the output reflect real change.
Weight of second (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. Weigh rather than estimate where you can — this field usually enters the formula multiplicatively.
Weight of third (example value 1) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Use the same conditions each time (same scale, same time of day) so that changes in the output reflect real change.
Convexity on the example inputs: the complete substitution
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: First value, Second value, Third value (use twice for 2-item blends), Weight of first. The computed convexity comes out at 113.75, which the interpretation band labels “Wide component spread — the average hides a lot”.
- Σv·w = 160.0 + 115.0 + 180.0 = 455.0
- ÷ Σw = 4 → 113.75
Simple mean — 125.00. Compare it against the main result of 113.75 before drawing conclusions.
Weight spread — 1.0. If your inputs change, this is usually the first companion figure to move.
Range of components — 100.00. This is the number experienced users quote when the headline alone would mislead.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
How far Convexity can reasonably move
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.
| Third value (use twice for 2-item blends) setting | Convexity |
|---|---|
| 80 % of the example value | 104.75 |
| 90 % of the example value | 109.25 |
| example inputs | 113.75 |
| 110 % of the example value | 118.25 |
| 120 % of the example value | 122.75 |
Across 5 settings of Third value (use twice for 2-item blends), the result spans 104.75 to 122.75. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Third value (use twice for 2-item blends) alone; the substitution steps will follow your figures exactly.
The levers behind Convexity, ranked by effect
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the convexity was recalculated from scratch. It is the fastest honest answer to “what matters most in Convexity?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Nudge Third value (use twice for 2-item blends) by ±10 % and Convexity lands between 109.25 and 118.25 (sensitivity ≈4.0 %)
- First value: ten percent up gives 117.75, ten percent down gives 109.75 — ≈3.5 % of the convexity either way
- Nudge Second value by ±10 % and Convexity lands between 110.88 and 116.63 (sensitivity ≈2.5 %)
- Weight of first: ten percent up gives 112.14, ten percent down gives 115.53 — ≈1.6 % of the convexity either way
- Weight of third +10 % → Convexity = 115.37 · −10 % → 112.05 (the convexity shifts ≈1.5 %)
- Nudge Weight of second by ±10 % and Convexity lands between 113.72 and 113.78 (sensitivity ≈0.0 %)
Third value (use twice for 2-item blends) is the dominant lever here: ten percent either way moves the result by about 4.0 %, from 109.25 to 118.25. Spend your verification effort there first, and treat First value as the second priority (≈3.5 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Is your Convexity good — reading the result bands
The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “Wide component spread — the average hides a lot”; your own figures place you on a different rung of the same ladder. The sensitivity list shows how far a modest input error moves you along that ladder: for Third value (use twice for 2-item blends), ±10 % covers 109.25 to 118.25. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
The comparison worth making is not with somebody else’s Convexity but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
Why Convexity results go wrong — and how to prevent it
Weights must share one unit (dollars, hours, kg); mixing units produces a number that is meaningless but still displays fine. 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.
Confusing annual with monthly rates. A "1 % per month" fee is roughly 12.7 % annualized; the calculator takes one convention, and picking the wrong one can misstate Convexity by double digits.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Third value (use twice for 2-item blends) first, everything else second.
Another is comparing across contexts: a Convexity computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Six things to confirm before acting on Convexity
- Compare the result with one independent method or published benchmark.
- Verify each input against its original source document, not memory.
- Re-verify Third value (use twice for 2-item blends) against a source document — ten percent of error there moves the headline by ≈4.0 %.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Confirm the example values are plausible for your own situation before replacing them.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
A routine for decision-grade Convexity
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 first value, second value, third value (use twice for 2-item blends), weight of first, weight of second, weight of third. 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. When two sources disagree, it is almost never the arithmetic that differs.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Convexity (113.75 for the example values), and note the verdict band. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Convexity from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 113.75 output. Six months from now the context is what turns this figure into a trend. If a result feels obviously right, that is the moment to check the inputs hardest.
Where Convexity matters in practice
In Interest & Rates the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. One decimal place more than your data supports is one decimal place of fiction.
The audience for this page is people who need one trustworthy number before their next decision. In professional Interest & Rates practice the pattern is always the same — screen with Convexity, then invest slow analysis only in whatever survives the screen. Rounding early is the quietest way to introduce a permanent error.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Finance & Banking the expensive mistakes are rarely sudden; they are small changes in First value that nobody recalculated for a year. The test of a good estimate is not that it feels right but that it changes what you do.
Quick answers: what searchers ask about Convexity
What affects Convexity the most?
Measured on this engine, Third value (use twice for 2-item blends) is the dominant lever: moving it ±10 % shifts the convexity across 109.25 to 118.25 — about 4.0 % of the headline, with First value next at ≈3.5 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: first value or third value (use twice for 2-item blends)?
By the numbers, Third value (use twice for 2-item blends): a ten-percent change in it moves the result ≈4.0 %, versus ≈3.5 % for First value. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
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 113.75 (Wide component spread — the average hides a lot). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Convexity by hand?
weighted average = Σ(value × weight) ÷ Σ weights is the entire method. Work the inputs in that order — Σv·w = 160.0 + 115.0 + 180.0 = 455.0 — and you will reach 113.75 on the default figures, the same number this tool prints.
What happens to Convexity if third value (use twice for 2-item blends) changes by 10 %?
On these inputs a ±10 % change in third value (use twice for 2-item blends) takes Convexity to 118.25 against the 113.75 example — around 4.0 % of the headline. The same test on every other field is in the sensitivity section.
Is the Convexity result of 113.75 good or bad?
The tool answers “what”, not “whether”: 113.75 carries the verdict “Wide component spread — the average hides a lot” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
What affects Convexity the most?
Sensitivity depends on where you start, but the inputs First value and Second value typically move Convexity further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Can Convexity be negative or empty?
Yes, and that is informative rather than broken: a negative Convexity usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
When does weighted beat simple?
Whenever components differ in importance or size — averaging three test scores of 1 and 4 credits needs the weights.
Can weights be percentages?
Yes — only the ratios matter; Σw need not equal 100.
Do I need an account to use this Convexity calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
What the labels on this page mean
- Simple mean
- 125.00 for the Convexity worked case; it sits next to the main result because it carries context the headline leaves out.
- Weight spread
- 1.0 for the Convexity worked case; it sits next to the main result because it carries context the headline leaves out.
- Range of components
- 100.00 on the example inputs — a companion figure printed beside the headline of Convexity so that no result is read in isolation.
- Convexity
- The primary output of this tool: 113.75 for the default inputs, computed exactly from weighted average = Σ(value × weight) ÷ Σ weights.
- Worked example
- Every substitution in order, from the example inputs to 113.75 — the audit trail for the headline figure.
- Verdict band
- The interpretation attached to a result (“Wide component spread — the average hides a lot” on these inputs), which turns a bare number into a position on a scale.
- 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.
Where the Convexity model comes from
The model is published arithmetic implemented exactly as written: weighted average = Σ(value × weight) ÷ Σ weights. Source of record: Weighted mean definition. 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.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
Turning this Convexity into a decision
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.