Compounding flywheel calculator
User manual
This calculator follows the productive life of your capital: contributions become invested capital, retained returns enlarge that capital, and the enlarged balance earns further returns.
1. Getting started
- Enter your initial capital and contribution amount per payment.
- Select how often you make that payment and the number of years to model.
- Set the nominal investment return, tax on gains, inflation, and percentage reinvested.
- Read the four results above the graphs. Results update automatically.
- Use the graph tick boxes and hover over either graph to inspect individual years. Check the audit table for the calculation details.
The current defaults are initial capital 0, contribution 1,000 annually, 40 years, nominal return 7%, tax 0%, inflation 2.5%, full reinvestment, and EUR. “Restore default inputs” restores these inputs.
The timing assumption matters: this version compounds annually. All recurring payments for a year are added at year-end. Monthly payments change the annual contribution total, but do not earn returns during the year they are contributed.
2. Understanding the inputs
| Input | Meaning |
|---|---|
| Initial capital | The money already invested at the start, before year 1. It earns returns in year 1 and counts as part of your lifetime contributions. Any non-negative amount, including decimals, is accepted up to 1 trillion. |
| Contribution per payment | The amount you supply on each recurring payment. For example, 1,000 monthly means 12,000 contributed per year. It remains fixed in nominal money. Any non-negative amount, including decimals, is accepted up to 1 trillion. |
| Contribution frequency | Annual: 1 payment; quarterly: 4; monthly: 12; fortnightly: 26; weekly: 52. The calculator multiplies the per-payment amount by this count and adds the total at year-end. |
| Timeline | A whole number of years from 1 to 100. “Not reached” means the crossover did not occur within this timeline. |
| Nominal annual return | The assumed yearly investment gain or loss before tax and inflation. The same rate is used each year. Allowed range: −100% to 100%, in steps of 0.1 percentage point. |
| Tax on positive gains | The percentage deducted from positive investment gains each year, from 0% to 100% in whole percentage points. It is a generic tax drag, not the tax law of any country. No tax deduction is applied to losses and no loss credit is granted. |
| Annual inflation | The assumed yearly change in prices. It converts future invested capital into starting-year purchasing power. Allowed range: −20% to 100%, in steps of 0.1 percentage point. Inflation does not reduce the nominal account balance. |
| % that is reinvested | The share of positive, after-tax gains that remains invested, from 0% to 100% in whole percentage points. At 100%, all net gains join the capital base. At 50%, half remains invested and half is withdrawn. Losses reduce capital in full regardless of this setting. |
| Display currency | Changes the currency label and formatting only. It does not convert amounts using exchange rates or change taxation. Choices include EUR, ZAR, USD, GBP, JPY, CNY, AUD, SGD, CHF, and currency units. |
Example: tax and reinvestment
If opening capital is 10,000 and the annual return is 7%, gross gains are 700. With 20% tax, 140 is deducted, leaving net gains of 560. With 50% reinvestment, 280 remains invested and 280 is withdrawn. A year-end contribution of 1,000 brings closing capital to 11,280.
3. Reading the graphs
How the percentage box connects to the graph
The “% that is reinvested” input is a percentage. It determines how much of each year's positive investment gains, after tax, remains invested. The “Reinvested capital” graph line shows the resulting accumulated money amount in the selected currency, rather than a percentage or just one year's reinvestment.
For example, if a year produces 800 in after-tax gains and the input is 50%, 400 remains invested and 400 is withdrawn. The retained 400 becomes part of the capital that can earn further returns. Over time, the graph accumulates those reinvested gains, including subsequent gains kept invested. Investment losses reduce this amount.
How the three capital lines fit together
- Lifetime contributions: the initial capital and all subsequent payments you supplied. Investment gains are excluded.
- Reinvested capital: accumulated investment gains kept invested after tax and withdrawals, including further retained gains earned on earlier gains, reduced by losses. Your own contributions are excluded.
- Total invested capital: the combined amount remaining invested at the end of the year.
If your lifetime contributions are 10,000 and your accumulated reinvested capital is 4,000, total invested capital is 14,000. These are two components and their combined total; adding all three lines together would count the same money twice.
The reinvested capital label follows the currency dropdown, for example “Reinvested capital (EUR)” or “Reinvested capital (ZAR)”. Changing the currency changes the labels and formatting only; it does not convert the amounts using exchange rates.
“Real invested wealth” is the inflation-adjusted purchasing power of the total invested capital. It is another way of expressing that same total, not a fourth source of capital to add to it.
Capital created by the flywheel: the accumulated stock
The upper graph answers “How much capital has been formed by this year?”
- Total invested capital: the closing portfolio balance, including contributions and retained investment gains.
- Lifetime contributions: initial capital plus all recurring contributions so far.
- Reinvested capital (selected currency): accumulated reinvested investment gains, calculated as invested capital minus lifetime contributions. The currency shown in the graph label follows the currency dropdown. Your own contributions are shown separately as lifetime contributions. This includes the returns earned on earlier reinvested returns and can be negative when losses occur.
- Real invested wealth: total invested capital adjusted for inflation, expressed in the purchasing power of the starting year.
Tick or untick each line independently. For a nominal view, untick real invested wealth. To compare nominal wealth with purchasing power, leave total invested capital and real invested wealth ticked. The hover tooltip shows values for the visible lines at the nearest whole year.
The upper graph's yellow marker identifies the cumulative crossover. It appears when that milestone is reached and the reinvested capital line is selected. Hiding a line changes the view, not the calculations or audit table.
Real wealth is an alternative valuation of the same portfolio, not extra capital. Do not add it to nominal capital. The other lines remain nominal; this graph does not calculate a separate real-gains-versus-real-contributions crossover.
Who supplies the new capital each year?: the annual flow
The lower graph answers “During this year, did I or the investment add more new capital?” It compares annual contributions with that year's retained, after-tax gains.
If you contribute 1,000 and retain gains of 300, your contribution supplies most of that year's new capital. If retained gains reach 2,500, the engine adds 2,500 while you add 1,000. Its yellow marker shows the annual crossover.
This explains a different dimension from the upper graph: the upper graph shows everything accumulated so far; the lower graph shows the additions in one year. Hover over either graph for a tooltip beside the mouse. Move away to hide it.
4. The two crossover points
| Milestone | Exact test | Interpretation |
|---|---|---|
| Annual crossover | Positive annual retained gains ≥ annual recurring contributions. | The invested capital supplies at least as much new capital that year as your recurring payments. |
| Cumulative crossover | Cumulative retained investment gains > lifetime contributions, including initial capital. | More than half of the invested balance has come from retained investment returns rather than your supplied capital. |
The annual test accepts equality; the cumulative test requires gains to exceed contributions. Both use nominal amounts and exclude withdrawn cash. Zero gains against zero contributions do not qualify. If contributions are zero but gains are positive, the annual test can qualify.
Markers identify the first qualifying complete year, not a precise date within the year. A drawn line may appear to intersect between years; the yellow marker refers to the annual observation used by the model. “Not reached” is limited to the chosen timeline.
With initial capital 0, annual year-end contributions of 1,000, return 7%, no tax, and full reinvestment, annual crossover occurs in year 12 and cumulative crossover in year 20. Inflation does not change these nominal crossover years.
Worked example: annual crossover reached, cumulative crossover not reached
A calculator result can show “Annual crossover point: Year 25” and “Cumulative crossover point: Not reached” at the same time. These results answer different questions, so they do not contradict each other.
In the example below, the selected timeline is 40 years. The upper graph shows the following accumulated amounts at the end of year 40:
| Source of invested capital | Amount | Share of total |
|---|---|---|
| Lifetime contributions: money supplied by the investor | €197,210 | Approximately 53% |
| Reinvested capital: accumulated gains kept invested | €175,102 | Approximately 47% |
| Total invested capital | €372,312 | 100% |
Why annual crossover is reached in year 25: the lower graph compares additions during a single year. In year 25, that year's after-tax, reinvested gains first equal or exceed that year's recurring contributions. From that point in this constant-return example, the investment supplies more new capital per year than the investor does.
Why cumulative crossover is not reached by year 40: the upper graph compares amounts accumulated over the entire journey. Reinvested capital of €175,102 is still below lifetime contributions of €197,210. The orange reinvested capital line has not yet overtaken the blue lifetime contributions line.
The investment can add more than you do each year while its accumulated gains are still catching up with everything you contributed in earlier years.
Think of the lower graph as this year's additions and the upper graph as the running totals. Annual crossover concerns one year's additions; cumulative crossover concerns the totals built up over all years.
“Not reached” means not reached within the selected 40-year timeline. It does not establish that crossover can never occur. Extending the timeline shows what happens under the same assumptions.
The purple real wealth line expresses the purchasing power of the same total invested capital after inflation. It is not another source of capital, and it does not determine either nominal crossover. Withdrawn cash is excluded from invested capital; this example shows no withdrawn cash.
These figures illustrate one scenario, not the default inputs or a forecast. Your own inputs determine your crossover years and amounts.
The annual capital threshold
For positive returns, the effective retained rate is nominal return × (1 − tax rate) × reinvestment fraction. The opening-capital threshold is annual contributions ÷ effective retained rate. For 1,000 annually, 7% return, no tax and full reinvestment, it is approximately 14,286. The first qualifying year's opening balance may exceed that threshold because the model advances in whole years.
5. How compounding is calculated
Each year's closing capital becomes the next year's opening capital. That is the recursive mechanism: reinvested gains earn returns alongside your original money and subsequent contributions.
Tax = positive gross gain × tax rate
Net gain = gross gain − tax
Retained gain = positive net gain × reinvestment fraction; a loss is retained in full
Withdrawn cash = net gain − retained gain
Closing capital = opening capital + retained gain + annual contributions
Real wealth = closing capital ÷ (1 + inflation rate)year
Use decimal fractions in these formulas: 7% is 0.07. When all gains are reinvested and there is no tax, the recurrence simplifies to closing capital = opening capital × (1 + return) + annual contributions.
| Year | Opening capital | Gain at 7% | Contribution | Closing capital |
|---|---|---|---|---|
| 1 | 0 | 0 | 1,000 | 1,000 |
| 2 | 1,000 | 70 | 1,000 | 2,070 |
| 3 | 2,070 | 144.90 | 1,000 | 3,214.90 |
In year 3, the previous gain of 70 itself earns 4.90. That return on a previous return is compounding.
Assumptions and scope
- Return, inflation, taxation and contribution amount are constant throughout the timeline.
- Contributions are added at year-end; there is no selectable monthly compounding model in this version.
- Tax is deducted annually from positive gains before reinvestment. Deferred tax, allowances, loss relief and tax on eventual disposal are not modelled.
- Withdrawn gains are tracked as nominal cash totals. They earn no further returns and are excluded from invested capital and real invested wealth. Their subsequent use is not modelled.
- No fees, contribution escalation, varying returns, investment risk simulation, pension benefit rules or exchange-rate conversion are included.
- The figures illustrate the specified assumptions. Actual returns can fluctuate, and an actual annual crossover can reverse in a later year.
6. Audit table, downloads and saved scenarios
Year 0 records your initial capital as a contribution. Each subsequent row records opening capital, annual contributions, gross gains, tax, net gains, retained gains, withdrawn cash, closing capital, lifetime contributions, cumulative retained gains, cumulative withdrawn cash, and real wealth. Yellow rows identify crossover milestones.
Two useful checks are closing capital = opening capital + retained gains + annual contributions, and closing capital = lifetime contributions + cumulative retained gains.
- Download audit CSV: saves the assumptions and year-by-year values for use in a spreadsheet. Lines beginning with # contain model settings. Displayed amounts are rounded to whole currency units; the CSV preserves greater precision.
- Save scenario: saves the current input values in this browser. One scenario is stored; saving again replaces it. Graph tick-box selections are not saved.
- Load saved scenario: restores those saved input values. It does not transfer scenarios between browsers or computers. Browser privacy settings may prevent saving, and clearing browser storage may remove the saved scenario.
- Restore default inputs: resets the input fields. It does not delete the saved scenario or reset graph tick boxes.
7. Common questions
Why does reducing reinvestment delay the crossover?
Less of each gain joins the invested capital. The balance grows more slowly, and less new capital is supplied by retained gains. At 0% reinvestment, positive gains are withdrawn and neither retained-gain crossover is reached.
Why does inflation not change the nominal capital line?
Inflation changes what money can buy, rather than the amount in the portfolio. The real wealth line shows this purchasing-power effect separately.
Why is there no gain in year 1 when initial capital is zero?
Your first recurring contributions arrive at the end of year 1 in this model. They begin earning returns in year 2.
What does an input error mean?
Check that the field is filled, within its allowed range, and uses the permitted increment. The timeline must be a whole number. Money fields accept decimals. Results are cleared while an input is invalid.
How do I use the calculator on another screen or computer?
Open flywheel-calculator.html in your browser and move that browser window to the other screen. To use it on another computer, copy both flywheel-calculator.html and flywheel-manual.html into the same folder. Both work offline. The manual link requires them to remain together.