How it works
First-month cash burn grows by a fixed percentage each subsequent month; spending is a geometric sum. This form solves for mathematical runway; enter the known quantities in Required starting cash (same currency), First-month cash burn (same currency), Monthly burn increase.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Required starting cash (same currency) | 61,051 | Formula symbol: cash. Enter a numeric value. Must be greater than zero. |
| First-month cash burn (same currency) | 10,000 | Formula symbol: burn. Enter a numeric value. Must be greater than zero. |
| Monthly burn increase | 10 % | Formula symbol: growth. Enter the percentage as a number: for 15%, enter 15. Use the monthly rate. Must be greater than zero. Allowed range: 0.001–100. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Required starting cash (same currency)
- 61,051
- First-month cash burn (same currency)
- 10,000
- Monthly burn increase
- 10 %
Complete example results
- Mathematical runway
- 5 mo
Reading the result
The result solves for mathematical runway from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the mathematical runway result?
Growth must be positive. The time solution is a continuous mathematical month equivalent; calendar payments need separate budgeting. New revenue or financing is excluded. All monetary inputs must use the same currency; currency conversion, tax and automatic fees are excluded. The source derives a finite geometric sum; here its first term is first-month burn and its common ratio is 1 plus monthly growth. A fractional month is the mathematical extension of that formula.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: openstax.org