Two schemes that answer the same question very differently
A state pension is not a pot of money with your name on it. It is an entitlement: you build up a record, and the state pays a rate it publishes. That means the arithmetic has no investment return in it at all, and it means the two countries covered here need entirely different questions asked of you, because they count entitlement in entirely different ways.
The United Kingdom counts years and nothing else. A qualifying year is a qualifying year whether you earned a little or a great deal, which makes the calculation a straight proportion and makes the answer easy to check. Germany counts pay: a year of contributions on exactly the national average earns one earnings point, half the average earns half a point, twice the average earns two — up to the ceiling above which no contributions are due and no further points accrue. The pension is then the points multiplied by the published value of a point.
The United Kingdom: a cliff, then a straight line
Below the minimum record the new State Pension pays nothing at all. This is a cliff rather than a taper and it is the single most useful thing this page can tell somebody with a short record: a few more qualifying years is the difference between nothing and something, and voluntary contributions to fill gaps are usually the best-value money available to anybody in that position.
Above the minimum, the pension is the full rate in proportion to your record, up to the number of years that earns the full rate. Each additional qualifying year is worth the same as every other one, which makes the trade easy to evaluate.
One large caveat applies to anybody whose record began before the new scheme started. Their entitlement is worked out from a starting amount calculated under both the old rules and the new, and it can be higher or lower than the simple proportion — higher for people with substantial Additional State Pension, lower for those who were contracted out. This page does not model that, which is why it points you at the official forecast.
Germany: points, and the factor for when you start
The points model makes the German pension unusually legible: you can see exactly what a year of your working life is worth, and the page shows the points per year as well as the total. What it cannot do is know your actual salary history. A form cannot ask for forty years of payslips, so the model assumes your pay held the same position relative to the national average for the whole record. For most careers that is roughly true in the middle and wrong at both ends, and it is the largest assumption on the page.
Starting the pension away from the standard age changes it permanently through the access factor: each month early costs a fixed fraction, each month deferred adds a slightly larger one. Which pension you may draw and from when is a separate body of rules — they depend on your birth year and on how long your record is — and this page does not model those. It applies the factor to whatever number of months you tell it.
The average-earnings figure for the current year is provisional under the law and is replaced by a settled figure about two years later, so a pension worked out with it moves slightly when that happens. The page says so when the figure it used is the provisional one.
Why the monthly figure is not four weekly payments
A weekly rate becomes a yearly one by multiplying by the number of weeks in a year, and a monthly one by dividing that by twelve. Treating a month as four weeks loses a payment or so a year and understates the monthly figure by several per cent. The page derives every cadence from the one the law actually states, so the three figures cannot disagree with each other.
What this does not do
It covers the state scheme only, not workplace or private pensions. For the United Kingdom it leaves out the pre-2016 basic State Pension, the Additional State Pension, contracting out and deferral increases. For Germany it leaves out credits for raising children, the supplement for long low-paid records, the pension for people with very long records, reduced earning capacity pensions and survivor benefits. It does not model tax on the pension, and both countries do tax it.