Pure Premium Calculator
Pure premium is the cornerstone of property and casualty ratemaking: the expected loss cost per exposure, before any expense or profit. This calculator uses the frequency-severity method, multiplying expected claim frequency by average severity to get the pure premium, then grossing it up with a fixed expense per exposure and a permissible loss ratio to produce an indicated rate. Frequency and severity come from your own trended loss experience, so they are user inputs rather than assumed figures.
Pure premium and rate formula
Pure premium = frequency * severity
Loss cost = pure premium + fixed expense per exposure
Indicated rate = loss cost / (permissible loss ratio / 100)
Loading share % = (indicated rate - pure premium) / indicated rate * 100
The permissible loss ratio equals 1 minus the variable expense and profit provision. Dividing the loss cost by it grosses up for variable expenses and profit to give the indicated rate.
Things to know
- Frequency and severity come from trended, developed loss experience for the rated segment.
- Pure premium excludes all expenses and profit; it is the expected loss per exposure.
- The permissible loss ratio is 1 minus the variable expense and profit provision.
- Fixed expenses per exposure are added before grossing up, not loaded by the ratio.
- Follow CAS ratemaking principles and ASOP guidance for formal rate filings.
Pure premium: frequently asked questions
What is pure premium in actuarial ratemaking?
Pure premium is the expected claim cost per exposure unit, with no provision for expenses or profit. It equals claim frequency times claim severity, or equivalently total losses divided by exposures. It is the foundation of the frequency-severity method used in property and casualty ratemaking.
How are frequency and severity defined?
Frequency is the expected number of claims per exposure unit, for example claims per policy-year. Severity is the average cost per claim. Their product is the expected loss per exposure, the pure premium. Splitting losses this way lets actuaries analyze and trend each component separately.
How do I turn a pure premium into a rate?
Divide the pure premium (plus any fixed expense per exposure) by the permissible loss ratio to gross it up for variable expenses and profit. The permissible loss ratio is 1 minus the variable expense and profit provision. This calculator reports the indicated rate using your permissible loss ratio.
What is the permissible loss ratio?
The permissible loss ratio is the share of each premium dollar expected to be available for losses after variable expenses and the profit provision. If variable expenses and profit total 35 percent, the permissible loss ratio is 65 percent. Enter it as a percentage; the rate is the loss cost divided by that ratio.
Why are frequency and severity user inputs?
Frequency and severity come from an insurer's own loss experience for the specific line, territory, and class being rated, adjusted for trend and development. They are not universal constants, so this tool takes them as inputs from your experience analysis rather than assuming any figure.
Official sources
- Casualty Actuarial Society: CAS ratemaking principles and study notes.
- Actuarial Standards Board: Actuarial Standards of Practice.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.