Tools

Marginal Rate Inside a Benefit Withdrawal Band

A benefit withdrawn as a percentage of income above a threshold adds a marginal rate proportional to the size of the benefit. How much does that add to the rate on your next unit of income, how much of it depends on how many units you receive the benefit for, and what contribution would remove it?

A benefit that is withdrawn gradually across a band of income is a marginal rate by another name. Every unit of income inside that band takes a share of the benefit with it, and the share is the benefit divided by the width of the band — so the rate is larger for somebody receiving a larger benefit, and the benefit is larger for somebody receiving it for more units. Two people on the same income, meeting the same band, therefore face different rates on the same next unit. That is the whole mechanism, and it is why the question has no single answer: the rate depends on a fact about the household that no table of tax bands carries.

What this tool does not decide

Which country you are in. All seven figures are yours. This page publishes no threshold, no band, no benefit amount, no withdrawal ratio and no tax rate, and there is no control to choose a country, a scheme or a year with. It describes a mechanism, not a jurisdiction.
Which of two people in a household is charged. The charge falls on the individual it is assessed on, so a household earning the same total split differently gets a different answer. There is one income field here and no rule in the mechanism for combining two.
What the rest of your marginal rate is. This is one mechanism. Any other charge, allowance, credit, threshold or taper the same income meets is not here, and a rate above one hundred per cent on this page may not be the whole of yours.
Whether to take the raise or make the contribution. The page publishes the rate and the contribution that would remove the charge. Which is worth more to you depends on more than one band, and none of the rest of it is in this arithmetic.
A cliff. Where a whole benefit goes at one point rather than across a band, this is the wrong calculator and the page says so rather than producing a number.

Your figures

The interactive calculation runs in your browser and needs local JavaScript, which is currently switched off. Activating the Calculate button does nothing at all: no request is sent and nothing is submitted.

Everything else on this page works without it. The model, the formulas, the timing convention, the worked example, the assumptions and the limitations are all in the methodology below, and the companion explainer covers the mechanism in full.

Your figures, in seven numbers

All seven figures are yours. This page publishes no threshold, no band, no benefit amount, no withdrawal ratio and no tax rate, and there is no field on it that could carry one — there is no country to choose, no scheme to select and no year to pick. Four of these seven are a published parameter somewhere, and the reason none of them is offered here is that offering one would make this a page about a jurisdiction rather than about a mechanism. Enter yours in one currency and over one period, all seven consistently, and every figure comes back in the same unit.

The income of the person the charge is assessed on

One person’s income, not a household’s. This mechanism assesses the individual the charge falls on, so a household total entered here would answer a question it does not ask — and there is no second income field, because there is no rule in the mechanism for combining two.

Contributions that reduce that income

Enter 0 if there are none. This is the lever the whole question turns on rather than a detail of it: the income the band is read against is what is left after these come out, so a contribution moves you through the band and a raise moves you the other way. The result publishes the further contribution that would remove the charge entirely.

The income at which withdrawal starts

Yours to state. This page publishes no threshold and has no list to choose one from, because a threshold belongs to a jurisdiction and this page describes a mechanism. Zero is admitted, and is the case where withdrawal starts at the first unit of income.

The income at which the benefit is fully gone

The other end of the band, and it has to be above the threshold. Two figures make a band, and its width is what decides how fast the benefit goes: the same benefit withdrawn across half the width adds twice the rate. A band of no width is a cliff rather than a taper, and a different calculator on this site is the model for that.

The benefit received for one unit

For one unit, over the same period as the income — not the total for all of them. The count is the next field, and keeping the two apart is what makes the second half of the question answerable. Enter 0 if no benefit is received; that is a real case and it is the one that shows what the band alone does.

How many units it is received for

Children, in the question this page was built from — but the arithmetic knows nothing about what a unit is. A whole number from 0 to 20. Zero is admitted and gives an added rate of exactly zero, which is an answer rather than an error.

The rate on your next unit of income before this

What your next unit of income already meets, before this clawback is applied. Yours to state: this page does not know it and will not assume one. Enter 0 if there is none. Both ends are admitted, and there is no rule relating this rate to the one the clawback adds — the two may come to more than 100%, and that is the finding rather than an error.

Result

A benefit withdrawn as a percentage of income above a threshold adds a marginal rate proportional to the size of the benefit. That is the whole mechanism, and the consequence is the part no table of tax bands carries: the effective rate inside the withdrawal band is not a single figure at all. It scales with the number of units the benefit is received for, because the benefit does — so two people on identical incomes, meeting identical bands, face different rates on the same next unit of income, and the difference is how many units they receive it for.

Nothing bounds the total at one hundred per cent, and reaching it does not take an extreme case. A band five thousand wide, a benefit of a thousand a unit, three units and a baseline rate of forty-five per cent add sixty percentage points, which is an effective rate of 105 per cent: the next thousand of income leaves that person fifty worse off than not earning it. Every figure in that example is ordinary. The rate is built per unit and multiplied by the count, so it rises with the count without limit and nothing in the arithmetic stops it at any particular value.

The income above is one person’s. This mechanism assesses the individual the charge falls on rather than the household they live in, and that is not a detail: a household earning eighty thousand between two people, split fifty-five and twenty-five, has half its benefit withdrawn and faces a sixty per cent rate on the next unit. The same household earning the same eighty thousand split forty and forty loses nothing and faces forty. Same total, same benefit, same band, different answer. There is no field on this page for a joint income, because there is no rule in this mechanism for combining two — and a field that accepted a total would have made the wrong reading the natural one.

Enter your seven figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

What the band does, whoever is standing in it

How wide the band is: Not yet calculated
What one unit adds to the rate inside the band: Not yet calculated
What the whole benefit adds inside the band — a fact about the band: Not yet calculated

Where you stand in it, and what that costs

The income the band is read against, after contributions: Not yet calculated
How far through the band that leaves you: Not yet calculated
The benefit itself, for that many units: Not yet calculated
How much of it has already gone: Not yet calculated
How much of it is left: Not yet calculated
The further contribution that would remove the charge: Not yet calculated
How much more income lands inside the band: Not yet calculated

The same figures, with a different number of units

The second half of the question, as a table. The rate the clawback adds is the rate for one unit multiplied by the count, so it rises in equal steps — and every row here is a separate calculation rather than one figure multiplied out.
Units the benefit is received for	The benefit itself	What the clawback adds	The rate on your next unit	What is left of that unit
0	Not yet calculated	Not yet calculated	Not yet calculated	Not yet calculated
1	Not yet calculated	Not yet calculated	Not yet calculated	Not yet calculated
2	Not yet calculated	Not yet calculated	Not yet calculated	Not yet calculated
3	Not yet calculated	Not yet calculated	Not yet calculated	Not yet calculated

Every amount here is in the unit you entered the income in, and this page names no currency. Every amount is over the same period, and this page names none — a benefit entered weekly against an income entered annually produces an arithmetically consistent answer to a question nobody asked. Every rate is a rate on the next unit of income rather than on the whole of it, so it is comparable with another marginal rate and not with an average one, and not with the share of your income anybody pays in total.

This is one mechanism and not a tax calculation. The model knows nothing about any other charge, allowance, credit, threshold or taper the same income might meet, and a reader whose effective rate is over one hundred per cent here may meet more elsewhere — so this page does not claim to have found the whole of anybody’s marginal rate. It is also not a view on what to do. Whether to take the raise, make the contribution or do neither depends on more than one band, and none of the rest of it is in this arithmetic.

This page has no view on what you should do with the figure it gives you. A contribution that removes this charge is not free — it is money you no longer have, held under whatever rules apply to wherever it went, and this page models none of them. A rate above one hundred per cent on the next unit is a fact about that unit and not a reason to refuse a raise, because the units below it are still yours. Nothing here is a recommendation to contribute, to earn less, to claim or to stop claiming, and there is no product named anywhere on this page.

How this is worked out

Why the rate is not one figure

A benefit withdrawn as a percentage of income above a threshold adds a marginal rate proportional to the size of the benefit. That sentence is the whole mechanism and it contains no jurisdiction — a threshold, a top of a band, a benefit and a count are four numbers, and they are yours.The consequence is the part no table of tax bands carries: the effective rate inside the withdrawal band is not a single figure at all. It scales with the number of units the benefit is received for, because the benefit does, so two people on identical incomes meeting identical bands face different rates on the same next unit of income.

Three rates, and only two of them are worked out here

The rate you already faced is something you told this page. It is in the total, so the total is not a figure this page established on its own — which is why all three are printed together and never one of them alone.
Which rate	How it is arrived at	Whose figure it is	When it applies
What the clawback adds	The benefit for one unit, divided by the width of the band, multiplied by the count	This mechanism’s. It is the figure the arithmetic here establishes	Applies inside the band, and is exactly zero outside it
The rate you already faced	Whatever you entered	Yours. This page does not know it, does not check it and will not assume one	Applies wherever you are standing
What your next unit meets	The two above, added together	Half yours. It contains your figure, so it is not something this page worked out on its own	Applies to the next unit of income, and to no other

There is a fourth number on the result and it belongs to none of the three:the band’s own rate, which is a property of the band rather than of you. It is the same figure whether you are standing below the band, inside it or past the top of it, and what applies to your next unit of income is the added rate — that figure inside the band, and exactly zero outside it. The two are shown under separate headings for that reason. A page that mixed them would tell a reader below the threshold that their next unit is taxed at a rate it is not.

The arithmetic

Write I for the income the charge is assessed on, D for the contributions that reduce it, T for the threshold, U for the top of the band, b for the benefit for one unit, n for the count andt for the rate you already faced. Seven lines, and the whole model:

A          = I − D                          the income the band is read against
W          = U − T                          the width of the band
p          = b ÷ W                          what one unit adds
r          = p × n                          what the whole benefit adds
withdrawn  = (b × n) × (A − T) ÷ W          clamped to the band, so it never exceeds the benefit
added      = r inside the band, 0 outside it
effective  = t + added

The rate is built per unit first and then multiplied by the count, rather than as the whole benefit divided by the width. The two are the same quantity to within a last bit, and the first is chosen because the claim this page exists to make is that doubling the count doubles the rate — which on that route is an identity of the arithmetic rather than a consequence of it, and can be checked at exact equality rather than within a tolerance.

The two boundaries, and why they are not symmetrical

The states describe your next unit of income rather than your last one, because the question is about a raise or a contribution. That makes the band open at the top and closed at the bottom, and the asymmetry is deliberate rather than inherited from a comparison.

The amount withdrawn is continuous across both boundaries and the rate is not. That is the mechanism rather than a defect: the amount is the accumulation of the rate, and an accumulation of a step has no step in it.
Where you are standing	What has been withdrawn	What your next unit meets	What removes the charge
Exactly on the threshold	Nothing has been withdrawn yet	The elevated rate — your next unit is the first one anything comes out of	The contribution that removes the charge is nothing rather than absent
Anywhere strictly inside the band	A share of the benefit, in proportion to how far through you are	The elevated rate	The distance from where you are back to the threshold
Exactly on the top of the band, or past it	The whole benefit has gone	The rate you stated — there is nothing left for the next unit to lose	The whole distance back to the threshold, which is what it would take to have the benefit again

Why the total has no ceiling

Nothing bounds the rate you already faced plus the rate the clawback adds at one hundred per cent, and reaching it does not take an extreme case.A band five thousand wide, a benefit of a thousand a unit, three units and a baseline rate of forty-five per cent add sixty percentage points, which is an effective rate of 105 per cent. The next thousand of income leaves that person fifty worse off than not earning it. Every figure in that example is ordinary and nothing has been pushed to the edge of any range. What is left of the next unit is published signed for exactly that reason: the negative number is the answer rather than an error, and clamping it at zero would have hidden the finding this page exists to publish.

One person, and the household that gets two answers

The charge is assessed on an individual rather than on a household, and that is not a detail. A household earning eighty thousand between two people, split fifty-five and twenty-five, has half its benefit withdrawn and faces a sixty per cent rate on the next unit; the same household earning the same eighty thousand split forty and forty loses nothing and faces forty.Same total, same benefit, same band, different answer. There is no field on this page for a joint income because there is no rule in this mechanism for combining two — and a field that accepted a total would have made the wrong reading the natural one. A reader who wants to compare two splits calculates twice, which is the honest shape of that question.

The limits this calculation imposes on itself

Every figure is yours. This page publishes no threshold, no band, no benefit amount, no withdrawal ratio and no tax rate, and there is no field on it that could carry one — so it describes a mechanism rather than a jurisdiction, and nothing in it can go out of date.
This is one mechanism and not a tax calculation. The model knows nothing about any other charge, allowance, credit, threshold or taper the same income might meet, so a reader whose effective rate is above one hundred per cent here may meet more elsewhere.
Every figure belongs to one person. The charge is assessed on an individual rather than on a household, and which of two people in a household that is decides the answer — which is why there is one income field here and no rule for combining two.
There is no period and no currency anywhere in this arithmetic. Every amount has to be in the same one, and a benefit entered weekly against an income entered annually produces a consistent answer to a question nobody asked.
A band of no width is refused rather than special-cased. The whole benefit going at one point is a cliff: the value jumps, the rate on the next unit is unchanged everywhere it is defined, and a different calculator on this site is the model for that mechanism.

What is not modelled

any country, tax authority, benefit, scheme or statute — none is named and there is no field for one
any threshold, band, benefit amount, withdrawal ratio or tax rate of ours; all seven inputs are yours
a household income, a joint income, a partner’s income, or any rule for combining two incomes
which of two people in a household the charge is assessed on, which is the question the mechanism itself answers by assessing a person
any rule for converting a withdrawn allowance into cash, which is a tax rule rather than arithmetic
any other charge, allowance, credit, threshold or taper the same income might meet
a cliff, notch or step — a band of no width is refused, and a different calculator on this site is the model for that mechanism
any indexation, uprating or forecast of any figure you enter
any conversion between periods; there is no annual, monthly or weekly anywhere in this arithmetic
whether you should take the raise, make the contribution, or do neither

The decision this page refuses to take — whether to take the raise or make the contribution — is a comparison of two uses of the same money, and what makes such a comparison like-for-like is taught in the explainer:how to compare two financial uses of money.

Go deeper

The decision this page will not take for you
How to Compare Two Uses of Money Without Fake Certainty
Why opportunity cost only exists relative to a real alternative, what makes a comparison like-for-like, why a higher annual rate can start behind, and why the option that ends higher is not automatically the one to choose.
This page prices one side of a choice: what your next unit of income actually meets. The other side is what the same money does if it goes into the contribution instead, and comparing the two like-for-like is a discipline of its own — which is what the explainer teaches.
Read the explainer: How to Compare Two Uses of Money Without Fake Certainty

Calculation model and corrections

Calculation model: Benefit Withdrawal Rate v1.0
Last reviewed: 28 August 2026
Whose figures these are: Yours, all seven. This page publishes no threshold, no band, no benefit amount, no withdrawal ratio and no tax rate, and there is no field on it that could carry one. There is no country to choose, no scheme to select and no year to pick — which is why nothing on this page can go stale, and why it can describe the mechanism without describing anybody’s jurisdiction
Why the rate is three figures and never one: Because two of them are different quantities and the third is yours. What the clawback adds is what this mechanism establishes; the rate you already face is something you told the page and it neither knows nor checks; and the effective rate is the two added together. A page that printed the effective rate alone would be handing you your own input back as though it had worked it out
What the band’s rate is, and whose it is not: The benefit divided by the width of the band, multiplied by the count. It is a property of the band rather than of you: it is the same number whether you are standing below the band, inside it or past it, and what applies to your next unit of income is the added rate, which is that figure inside the band and zero outside it
Why the rate is built per unit: Because the second half of the question is whether the rate depends on how many units the benefit is received for. It is built as the benefit for one unit divided by the width of the band, and then multiplied by the count — so doubling the count doubles the rate exactly rather than approximately, and the ladder showing neighbouring counts is a set of separate calculations rather than one figure multiplied out
One person, not one household: Every figure belongs to the person whose income was entered. This mechanism assesses an individual, so a household earning the same total split differently gets a different answer, and there is no field here for a joint income because there is no rule in the mechanism for combining two
Where the band starts and where it ends: The band is entered at the threshold and left at the top, and the boundary is read for your **next** unit of income rather than your last. Standing exactly on the threshold, nothing has been withdrawn yet and the elevated rate is what your next unit meets. Standing exactly on the top, everything has gone and there is nothing left for the next unit to lose, so the rate is back to the one you stated
How much has already gone: The benefit multiplied by how far through the band you are, which is a share between nothing and all of it. It is continuous across both boundaries even though the rate is not — the amount withdrawn is the accumulation of the rate, and an accumulation of a step has no step in it
What removes the charge: A further contribution that reduces the assessed income back to the threshold. The figure published is the whole distance from where you are, not from the top of the band, and it is nothing rather than absent for somebody standing exactly on the threshold — a contribution of nothing is what it takes to leave a band you have only just entered
A rate above one hundred per cent: Is published rather than clamped, and what you keep of the next unit is published signed. Nothing in this mechanism bounds the total at one: the rate rises with the count without limit, and an ordinary set of figures reaches it. A negative figure for what you keep means your next unit of income leaves you worse off than not earning it
The unit and the period: Whatever unit you entered the income in, throughout, and whatever period. This page names neither and has no field for either, so every amount you enter has to be in the same currency over the same period — a benefit entered weekly against an income entered annually gives a consistent answer to a question nobody asked
Excluded: Every other charge, allowance, credit, threshold and taper the same income might meet; any rule for converting a withdrawn allowance into cash; any cliff, notch or step; any indexation or uprating; and any view on whether to take the raise or make the contribution
Rounding: Display only; intermediate values remain unrounded

Correction history

The contribution that removes the charge is nothing rather than absent for a reader standing exactly on the threshold, and the two are different answers. It was noticed while the boundary vector was being written rather than while the invariants were, and it is the one place where the half-open band and the rule about which figures may be absent have to be read together to get the right answer. A page that treated “nothing” and “there is no such figure” as the same thing would be wrong about which side of the boundary the reader is standing on — so this page prints a figure of zero where the model publishes one, and prints words only where the model publishes no figure at all.
The added rate was specified as the benefit for one unit divided by the width of the band and then multiplied by the count, rather than as the whole benefit divided by the width. The two are the same quantity to within a last bit, and the first was chosen because the claim this model exists to make is that doubling the count doubles the rate — which on the first route is an identity of the arithmetic rather than a consequence of it, and can therefore be asserted at exact equality rather than within a tolerance. The per-unit rate is published as well as the total for the same reason: a reader with no units who is considering having one is answered by it, and recovering it by dividing the total by the count is undefined at a count of zero, which this model admits.