What is the chain ladder method?

The standard way of estimating what an insurer will end up paying on claims that have already happened. The claims are laid out as a triangle, one row per origin period and one column per development age. Read down each pair of columns for the age to age ratios, select one factor per pair, multiply the selected factors from an age onwards to get a cumulative development factor, then multiply an origin period’s latest figure by its own cumulative factor. That product is the projected ultimate, and ultimate minus what has been booked so far is what is still to come.

How do you select a development factor?

There is no arithmetic answer, which is why it is the question you get asked. This page shows 3 selections side by side and marks the one in force: All-year volume weighted; Latest three, volume weighted; Simple average of the ratios. Volume weighting lets a large origin period count for more than a small one, a simple average gives every period the same vote, and taking the latest three stops an old year voting at all. Any column can also be overridden with a factor you type yourself. An origin period may only take part in a column when it has both of that column’s figures: letting a young year into the denominator with nothing above it is what produces a factor below 1 and a book whose claims appear to run backwards, so this page leaves that period out of the sum instead. Where a factor below 1 survives that, the commentary leads on it, because on cumulative claims it usually means a cell holds an incremental amount, a figure is out of order, or a real recovery is in there.

What is the difference between the total reserve and IBNR?

On a paid triangle, ultimate minus paid to date is everything still to be paid: the case reserves the claims team already holds, plus IBNR. The IBNR on its own is this figure minus those case reserves. On an incurred triangle, case reserves are already inside the figures, so ultimate minus incurred to date is the IBNR on its own. Calling the paid answer IBNR double counts the case reserves, so the label above the figure changes with the basis you choose.

Do I need a tail factor?

Only if the claims develop past your last column, which on a long-tail class they usually do. The tail starts at 1.000 here, which is the assumption that nothing develops after the last age you have typed, and a period that has already reached that age then shows nothing left to come. A tail comes from a curve fitted through the observed factors, from benchmarks for the class, or from a documented judgement anchored on both. Expect to be asked which of the three yours is.

Is the triangle I paste uploaded or stored anywhere?

No. The grid and the paste box are read in your browser and nothing is sent anywhere: no upload endpoint, no account, and no saved copy, not even in the browser’s own storage. Close the tab and your triangle is gone. That is enforced rather than promised, because a test reads this page’s own client component and fails on the sight of a request, a form or a browser store.

Free tool · nothing uploaded

Reserving triangle playground

Type a claims triangle, paste one out of your own spreadsheet or load a worked example, and watch the chain ladder run one step at a time: every age to age ratio, the factor selected from them, the chained factors, the projected ultimates and what is still to come.

3
factor selections: 2
worked examples: None
data uploaded

Worked example

Three accident years of cumulative paid claims, the triangle worked by hand, in Excel and in Python in our free chain ladder lesson.

What the figures are

It changes what the last column is called, and that matters: on paid figures the answer is the whole reserve, on incurred figures it is IBNR alone.

Units

Whatever your sheet is in. The ladder is scale free, so the units only ever label the headings.

Your triangle, cumulative, in £000s

Oldest period on top · blank cells are the future, not zeroes

An editable cumulative claims triangle. Rows are origin periods, oldest first, columns are development ages, and each cell is the total claims paid or incurred by that age.
Origin

Paste your own triangle

Copy the block of cells out of Excel or Google Sheets and paste it here. Tabs, commas, currency symbols and thousands separators are all read. A four-digit year in the first column is read as a label. Keep the oldest origin period on the first row, which is how a triangle is normally laid out, and the page says so if the labels arrive the other way up. It is parsed here and it never leaves your browser: there is no upload, no account and nothing saved, on this page or anywhere else. Close the tab and it is gone.

How the factor is selected

Total the column you are moving to, total the column you came from over the same origin periods, then divide. A large period counts for more than a small one.

Tail factor

One more multiplier for all the development past your last column. 1.000 means you are assuming there is none, which on a long-tail class is an assumption rather than an observation.

Step one: age to age ratios

Every origin period’s own ratio between each pair of development ages, the three candidate selections, and the factor actually applied.
Origin period	12 months to 24 months	24 months to 36 months
2023	1.500	1.100
2024	1.500
2025
All-year volume weightedin force	1.500	1.100
Latest three, volume weighted	1.500	1.100
Simple average of the ratios	1.500	1.100
Type your own factor
Selected factor	1.500	1.100

Step two: chain them together

The cumulative development factor from each age to ultimate, and the share of ultimate a period has reached by that age.
At this age	12 months	24 months	36 months
Cumulative factor to ultimate	1.650	1.100	1.000
Share of ultimate reached	60.6%	90.9%	100.0%

Each figure is every selected factor from that age onwards multiplied together, times the tail of 1.000. The share below it is one divided by that, which is the sentence to have ready: a factor of 1.607 means about 62% of the eventual total is in already.

Step three: ultimates and what is still to come

Each origin period’s latest figure, the cumulative factor applied to it, its projected ultimate and the amount still to come.
Origin period	Latest age	Paid to date	Factor to ultimate	Projected ultimate	Total reserve	Developed
2023	36 months	660.0	1.000	660.0	0.0	100.0%
2024	24 months	675.0	1.100	742.5	67.5	90.9%
2025	12 months	480.0	1.650	792.0	312.0	60.6%
Total		1,815.0		2,194.5	379.5	82.7%

Figures in £000s, on the units you typed them in. On a paid triangle the last column is everything still to be paid: the case reserves the claims team already holds, plus IBNR. The IBNR on its own is that figure minus those case reserves. This is a demonstration of the chain ladder on numbers you supplied, not a reserve estimate.

Development by origin periodSolid: observed · dashed: projected · £000s

What an interviewer would ask about this result

Read off your own numbers above. Nobody in a reserving interview asks you to do the arithmetic; they ask what you would do about what it shows.

Some factors rest on a single origin period: 24 months to 36 months is built from one origin period, so it is an observation, not an average. The question is what you would do about it: a benchmark for the class, a curve fitted through the earlier factors, or a judgement you can defend, and in every case you say which.
Most of the answer is one origin period: 2025: 2025 holds 82.2% of the total, and it is only 60.6% developed. That concentration is normal: the least developed periods are the ones with the most development still ahead of them. It is also where the method is least reliable, which is the honest answer when someone asks how confident you are.
The method reads every pound paid as evidence of a bigger year: 2025 carries a cumulative factor of 1.650, the largest on your triangle, so one more pound paid there becomes about 1.65 pounds of ultimate. The chain ladder cannot tell a bigger year from the same-sized year paying out faster. Naming that, and naming Bornhuetter-Ferguson as the method that dilutes it with an exposure-based expectation, is the answer to the most common follow-up in a reserving interview.
You have assumed nothing develops after 36 months: With the tail at 1.000 every origin period is treated as finished at 36 months, so a period that has already reached 36 months shows nothing left to come at all. On a long-tail class, liability or motor bodily injury, that is an assumption rather than an observation, and it is the one a reviewer challenges first. Try a tail of 1.05 and watch what happens to those periods.
What the reserve figure includes: On a paid triangle, ultimate minus paid to date is everything still to be paid: the case reserves the claims team already holds, plus IBNR. The IBNR on its own is this figure minus those case reserves.

The next method, and the one that answers the leverage problem above: Bornhuetter-Ferguson in the general insurance course.

What this tool does

A general insurer knows what it has paid so far and not what it will end up paying. Claims are reported late, settle slowly and get revised, so the year a policy was written can stay open for a decade. A development triangle is how that is laid out: one row per origin period, usually an accident year, and one column per development age, showing the total claims paid or incurred by the time that year was twelve, twenty four or thirty six months old. Recent years have reached fewer ages than old ones, which is what makes the shape a triangle. The missing lower right corner is not missing data. It is the future, and estimating it is the job.

The chain ladder is the standard way of doing that, and it is the method that comes up in almost every general insurance graduate interview. This page runs it on your numbers and shows every intermediate figure rather than a single answer, because the intermediate figures are where the judgement is and they are what you get asked about.

How it works, in three steps

One: age to age ratios. Read down a pair of columns rather than across a row. Each origin period that has both figures gives a ratio: how much that cohort grew between those two ages. An origin period may only take part if it has both. Letting a young year into the denominator with nothing above it produces a factor below one and a book whose claims appear to run backwards, which is the most common way a triangle is got wrong in a spreadsheet, and this page reports it instead of printing it.

Two: select one factor. Those ratios disagree, so somebody has to choose. Volume weighting sums the column you are moving to and the column you came from and then divides, which lets a large origin period count for more than a small one. A simple average gives every period the same vote whatever its size. Taking only the latest three stops an old year voting at all. All three are shown side by side, the one in force is marked, and any column can be overridden with a factor you type yourself.

Three: chain them and project. Multiply the selected factors from an age onwards and you have the cumulative development factor from that age to ultimate. Multiply an origin period’s latest figure by its own cumulative factor and you have its projected ultimate. Subtract what has been booked so far and what is left is the amount still to come. One divided by the cumulative factor is the share of the eventual total already in, which is the sentence worth having ready: a factor of 1.607 means about 62% of the final figure has arrived.

What it assumes

Four things, and each of them is a question you should expect. That the past development pattern will repeat, which fails when claims handling, case reserving strength, mix of business or the legal environment changes. That every origin period follows the same pattern, which is why a year that behaves differently is worth asking the claims team about rather than smoothing away. That the latest figure is the best starting point, which gives the method heavy leverage on the youngest period: every extra pound paid is read as evidence of a bigger year rather than of the same year paying faster. And that nothing develops after your last column, unless you set a tail. On a long-tail class the tail is the assumption that gets argued about most, so it is an explicit input here that starts at 1.000 and says what it is doing.

The tool is deliberately quiet about which selection is right, because that is not an arithmetic question. Two defensible selections on the same triangle can move the answer by more than the choice of averaging method ever does, and only knowing what happened in the year explains which is correct.

Reserve or IBNR: the distinction that gets checked

On a paid triangle, ultimate minus paid to date is everything still to be paid: the case reserves the claims department already holds on the claims it knows about, plus IBNR, the claims that have happened and not yet been reported along with expected growth on the ones already open. On an incurred triangle, paid plus case reserves, the case reserves are inside the figures already, so ultimate minus incurred is the IBNR on its own. Calling the paid answer IBNR double counts the case reserves. The basis selector above changes the label for exactly that reason, and real teams project both bases and interrogate the gap between them.

Where the numbers come from

There is no external figure on this page. Every number on screen is arithmetic on numbers you supplied, and the method is standard actuarial technique. Both worked examples are our own, taken cell for cell out of the general insurance course, and a test reads those lesson files and fails if the tool and the lesson ever disagree about the same triangle. What you paste is parsed in your browser: there is no upload endpoint, no account and nothing stored, and a test reads the page’s own source to keep it that way.

Three outside references are named on this page, and each was read from the publisher’s own page on 10 September 2026. The technique sits inside the profession’s own curriculum: General Insurance Reserving and Capital Modelling Principles (SP7) is the IFoA subject whose stated aim is the ability to apply, in simple reserving and capital modelling situations, the mathematical and economic techniques and the principles of actuarial planning and control needed for the financially-sound operation of general insurers. Institute and Faculty of Actuaries, General Insurance curriculum. The library a reserving team would reach for is open source, so the professional version of this arithmetic is not a secret: chainladder-python, in the Casualty Actuarial Society's GitHub organisation, describes itself as actuarial reserving in Python, triangle data manipulation, link ratios calculation, and IBNR models. casact/chainladder-python on GitHub. And the standard that governs the real version of the work is TAS 200: TAS 200: Insurance v2.0, effective from 1 January 2025, contains the requirements for technical actuarial work in relation to insurance and must be applied by all members of the Institute and Faculty of Actuaries for technical actuarial work in its scope. Financial Reporting Council, TAS 200: Insurance.

All three last checked 10 September 2026.

What this is not

This is a demonstration of a method, not a reserve estimate. Setting an insurer’s reserves is technical actuarial work under TAS 200, and real reserving runs several methods against each other, reads the incurred triangle beside the paid one, brings claims and underwriting into the room, tests the tail, and documents every selection for a reviewing actuary and a reserving committee. A page that multiplies your own figures together does none of that. Use it to learn the mechanics and to rehearse talking about them, which is what it is for.

Questions people ask about the chain ladder

What is the chain ladder method?: The standard way of estimating what an insurer will end up paying on claims that have already happened. The claims are laid out as a triangle, one row per origin period and one column per development age. Read down each pair of columns for the age to age ratios, select one factor per pair, multiply the selected factors from an age onwards to get a cumulative development factor, then multiply an origin period’s latest figure by its own cumulative factor. That product is the projected ultimate, and ultimate minus what has been booked so far is what is still to come.
How do you select a development factor?: There is no arithmetic answer, which is why it is the question you get asked. This page shows 3 selections side by side and marks the one in force: All-year volume weighted; Latest three, volume weighted; Simple average of the ratios. Volume weighting lets a large origin period count for more than a small one, a simple average gives every period the same vote, and taking the latest three stops an old year voting at all. Any column can also be overridden with a factor you type yourself. An origin period may only take part in a column when it has both of that column’s figures: letting a young year into the denominator with nothing above it is what produces a factor below 1 and a book whose claims appear to run backwards, so this page leaves that period out of the sum instead. Where a factor below 1 survives that, the commentary leads on it, because on cumulative claims it usually means a cell holds an incremental amount, a figure is out of order, or a real recovery is in there.
What is the difference between the total reserve and IBNR?: On a paid triangle, ultimate minus paid to date is everything still to be paid: the case reserves the claims team already holds, plus IBNR. The IBNR on its own is this figure minus those case reserves. On an incurred triangle, case reserves are already inside the figures, so ultimate minus incurred to date is the IBNR on its own. Calling the paid answer IBNR double counts the case reserves, so the label above the figure changes with the basis you choose.
Do I need a tail factor?: Only if the claims develop past your last column, which on a long-tail class they usually do. The tail starts at 1.000 here, which is the assumption that nothing develops after the last age you have typed, and a period that has already reached that age then shows nothing left to come. A tail comes from a curve fitted through the observed factors, from benchmarks for the class, or from a documented judgement anchored on both. Expect to be asked which of the three yours is.
Which IFoA exam covers reserving?: General Insurance Reserving and Capital Modelling Principles (SP7) is the IFoA subject whose stated aim is the ability to apply, in simple reserving and capital modelling situations, the mathematical and economic techniques and the principles of actuarial planning and control needed for the financially-sound operation of general insurers. That aim was read from the IFoA’s own general insurance curriculum page on 10 September 2026. The curriculum page does not name the chain ladder itself and the syllabus document behind it could not be read, so nothing here puts the technique on a syllabus we have not seen.
Is a projection from this page a reserve estimate?: No. It is a demonstration of a method on figures you supplied. TAS 200: Insurance v2.0, effective from 1 January 2025, contains the requirements for technical actuarial work in relation to insurance and must be applied by all members of the Institute and Faculty of Actuaries for technical actuarial work in its scope. Real reserving runs several methods against each other, reads the incurred triangle beside the paid one, brings claims and underwriting into the room, tests the tail, and documents every selection for a reviewing actuary.
Is the triangle I paste uploaded or stored anywhere?: No. The grid and the paste box are read in your browser and nothing is sent anywhere: no upload endpoint, no account, and no saved copy, not even in the browser’s own storage. Close the tab and your triangle is gone. That is enforced rather than promised, because a test reads this page’s own client component and fails on the sight of a request, a form or a browser store.

Learn the method properly

The lesson behind this tool works the same triangle by hand, then in a spreadsheet, then in twenty lines of Python, and it is free to read. The reserving module around it covers why claims take years, how to read a triangle, the chain ladder and the Bornhuetter-Ferguson method that answers the leverage problem the commentary above keeps raising.

Read the free chain ladder lesson →See the general insurance course →

Interviewing soon? The general insurance interview cheatsheet covers the reserving questions this tool prepares you for, alongside pricing, capital and the market.

Every free tool we have built is on the free tools page.