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SaaS Lifetime Gross Profit Model Calculator

Model account gross profit using monthly revenue, churn and linear account expansion.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Edit a calculated value to solve backwards, or lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

At monthly revenue of 100 per account, an 80% gross margin, 5% monthly churn and no expansion, the model gives lifetime gross profit of 1,600 per account.

Modeled months = 1 ÷ monthly churn; LTV = margin × months × [ARPA + monthly expansion × (months − 1) ÷ 2]

Worked example

Enter these known values and leave the other values blank.

Average revenue per account (ARPA)
100 USD
Gross margin
80 %
Churn
5 %
Account expansion
0 USD
Customer lifetime value (LTV)
1600 USD

Assumptions and limitations

  • This model applies a fixed monthly revenue increase over a modeled lifetime of 1 ÷ churn months. It is a linear expansion approximation, not a cohort survival model. Use a positive monthly churn fraction; acquisition costs, overhead and discounting are excluded.
  • Use consistent periods, currency and accounting definitions. The result follows the stated formula and the figures you supply.

Common questions

How does the expansion assumption work?

This model applies a fixed monthly revenue increase over a modeled lifetime of 1 ÷ churn months. It is a linear expansion approximation, not a cohort survival model. Use a positive monthly churn fraction; acquisition costs, overhead and discounting are excluded.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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