Capital Recovery Factor Calculator
The capital recovery factor turns a lump sum today into the equal payment needed to recover that amount, with interest, over a set number of periods. It is the engine behind loan amortisation, equipment lease pricing, and the annualised cost of a capital investment. This calculator takes the present amount, the interest rate per period, and the number of periods, then returns the capital recovery factor and the level periodic payment. The interest rate is a user input because it depends on your loan or discount assumption.
Capital recovery factor formula
i = rate per period as a decimal
CRF = i * (1 + i)^n / ((1 + i)^n - 1)
If i = 0, CRF = 1 / n
Payment = present amount * CRF
n is the number of periods and i is the periodic interest rate. The CRF is the reciprocal of the present-value annuity factor, so it converts a present amount into a level payment stream.
Where the CRF is used
- It produces the level payment for a fully amortising loan or mortgage.
- It annualises the upfront cost of capital equipment for cost comparisons.
- It prices fixed annuities by turning a present value into equal payments.
- Match the rate and number of periods to your payment frequency.
- When the rate is zero, the payment is simply the amount divided by n.
Capital recovery factor: frequently asked questions
What is the capital recovery factor?
The capital recovery factor (CRF) is the ratio that converts a present value into a stream of equal end-of-period payments over a fixed number of periods at a given interest rate. Multiplying a present amount by the CRF gives the level payment, like a loan amortisation or annuity payment, that exactly recovers the principal plus interest.
What is the capital recovery factor formula?
CRF = i * (1 + i)^n / ((1 + i)^n - 1), where i is the interest rate per period (as a decimal) and n is the number of periods. The annual payment equals the present value times the CRF. When i is zero, the CRF reduces to 1/n.
How does CRF relate to a loan payment?
A standard fully amortising loan payment is the loan principal multiplied by the capital recovery factor. So if you know the present amount, the periodic rate, and the number of periods, the CRF directly gives the level payment that pays off the loan over its term.
What is the difference between CRF and the annuity factor?
The capital recovery factor is the reciprocal of the present-value annuity factor. The annuity factor turns a stream of equal payments into a present value, while the CRF turns a present value into the equal payment. Multiplying the two together gives one.
What rate should I enter?
Enter the interest rate per period that matches your payment frequency. For monthly payments, use the monthly rate (annual rate divided by 12) and set n to the number of months. For annual payments, use the annual rate and set n to the number of years.
Official sources
- U.S. Securities and Exchange Commission: Compound interest.
- Consumer Financial Protection Bureau: What is amortization.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.