The SaaS Churn Rate & Customer LTV Sizer calculates fundamental unit economics for subscription software and SaaS recurring revenue business models.

### Subscription Economics Formulas - Customer Lifespan: Average retention duration in months is the reciprocal of monthly churn: $$\text{Lifespan (Months)} = \frac{1}{\text{Monthly Churn \% } / 100}$$ - Customer Lifetime Value (LTV): Evaluates gross profit generated per customer over their retention lifecycle: $$\text{LTV} = \frac{\text{ARPU} \times (\text{Gross Margin \% } / 100)}{\text{Monthly Churn \% } / 100}$$ - LTV-to-CAC Ratio: Compares customer lifetime value to Customer Acquisition Cost ($$\text{Ratio} = \text{LTV} / \text{CAC}$$). Venture capital benchmarks target $3.0\times$ or greater for sustainable economics. - CAC Payback Period: Months required to recoup sales and marketing acquisition spend: $$\text{CAC Payback (Months)} = \frac{\text{CAC}}{\text{ARPU} \times (\text{Gross Margin \% } / 100)}$$

### Worked Numeric Example - Monthly Churn Rate: 3.5% - Average Revenue Per User (ARPU): $49/month - Gross Margin: 80% (Gross profit per user = $49 × 0.80 = $39.20/month) - Customer Acquisition Cost (CAC): $250 - Performance Metrics: - Customer Lifespan: $1 / 0.035 = 28.6\text{ months}$ - Customer Lifetime Value (LTV): $39.20 / 0.035 = $1,120 - LTV-to-CAC Ratio: $1,120 / $250 = 4.5\times$ (Healthy Unit Economics) - CAC Payback Duration: $250 / $39.20 = 6.4\text{ months}$

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