The tax wedge on units that still trade becomes government revenue — a transfer, not a loss. The wedge on units that stop trading is deadweight loss: surplus destroyed and captured by no one. Together they are the total burden the wedge places on the affected quantity.
Component
Units affected
Per-unit wedge
Amount
Captured by
Tax revenue (transfer)
80
$4.00
$320
Government
Deadweight loss
20
avg $2.00
$40
No one (destroyed)
Total burden on the wedge
100
—
$360
—
Enter the size of the tax and the quantities traded before and after it, and the calculator sizes the welfare triangle lost to society alongside the revenue the tax actually raises.
Calculated in your browser — the numbers you enter are never sent to our servers.
What it calculates: Deadweight Loss, Tax Revenue, Quantity Reduction.
The $320 the government collects and the $40 nobody does
A $4 per-unit tax that cuts trade from 100 units to 80 does two entirely different things at once, and only one of them destroys anything. On the 80 units that still change hands, $4 each moves from buyers and sellers to the treasury: $4 × 80 = $320. Surplus changes pockets, but nothing evaporates — economists call that a transfer, and it is why the tax revenue figure sits beside the headline number rather than being added into it.
Deadweight Loss = ½ × Tax per Unit × (Quantity before − Quantity after)
On the 20 units that stopped trading, something is genuinely gone. Each of those trades was worth more to the buyer than it cost the seller, so each one would have created surplus; after the wedge none of them happen, and that surplus accrues to nobody at all. Sizing it is the whole job of this page: Deadweight Loss = ½ × Tax per Unit × (Quantity before − Quantity after), which here is ½ × $4 × 20 = $40.
The half is not a fudge factor. The first unit to be abandoned was only just worth trading, so the gain it would have produced was close to nothing, while the last one dropped was worth almost the full $4 wedge more to its buyer than to its seller. Averaged across the 20 lost units the destroyed surplus is about $2 apiece, which is exactly the average wedge shown in the decomposition table above.
Add the two pieces and the $4 tax places $360 of total burden on this market: $320 that someone still holds and $40 that no one does. The ratio matters more than either figure on its own. Here $8 of transfer accompanies every $1 of waste, which is why the waste is so easy to overlook — and why it is the number that welfare arguments are actually about.
Where the before and after quantities actually come from
The tax box is usually the easy input. The two quantity boxes are where the work is, and there are three honest ways to fill them.
In a textbook or exam problem, read them straight off the diagram. The before quantity is the competitive equilibrium where supply meets demand; the after quantity is the point where the vertical gap between the two curves equals the tax. Those are the only two quantities the triangle needs — the prices themselves never enter the formula.
If you are working from an elasticity instead, get there in two steps. Multiply the price elasticity of demand by the percentage rise in the price buyers actually pay — which equals the tax only when sellers pass all of it on — to get the percentage fall in quantity, then apply that percentage to the pre-tax quantity. A price elasticity calculator does the first step; this one does the second.
With real market data, the before quantity is observed volume in a period before the wedge and the after quantity is volume once it is in force. That route is the most convincing and the most fragile, for the reason set out at the end of this page.
Two mechanical checks before you trust the output. The tax must be per unit of the same thing the quantities count: a per-litre levy entered against quantities measured in cases produces a triangle with no meaning. And both quantities must sit on the same time basis, because the result inherits it — with 100 and 80 read as units per month, the $40 is $40 of waste per month, not a one-off.
Enter the same quantity twice and the triangle collapses to zero
Type 100 into both quantity boxes and the calculator returns a quantity reduction of 0, a deadweight loss of $0, and tax revenue of $4 × 100 = $400. Nothing has gone wrong. That is the perfectly inelastic case, and it is the cleanest illustration of what the triangle measures: with no trades abandoned there is no destroyed surplus, and the entire $400 is a transfer.
Markets approach this whenever buyers or sellers have nowhere else to go — goods with no close substitute, habitual purchases over a short horizon, land whose supply cannot expand. A lump-sum charge that does not vary with quantity is the limiting version: it changes no one’s trading decision, so it opens no triangle at all.
This is the entire efficiency case for taxing inelastic bases, and it is worth being precise about how narrow that case is. It is an argument about waste, not about fairness. The goods people cannot do without are frequently the inelastic ones, so the tax that scores best on this page can easily be the one that lands hardest on the households least able to absorb it. The calculator has nothing to say about that trade-off; it reports the triangle and stops.
The mirror of the zero case is worth knowing too. If you enter an after-tax quantity larger than the before-tax one, the tool floors the quantity reduction at zero rather than reporting a negative triangle, so the deadweight loss still reads $0. Check that your two quantities are the right way round before concluding that a wedge was costless.
The same $4 tax, two goods, and a tenfold gap in waste
Elasticity is the variable this calculator never asks for and yet depends on completely. It arrives entirely through the gap between your two quantities, so the fastest way to see what it does is to hold the tax fixed and move only the after quantity.
Keep the tax at $4 and the before quantity at 100. In a responsive market where trade falls to 80, the triangle is ½ × $4 × 20 = $40 and revenue is $4 × 80 = $320. In an unresponsive one where trade only slips to 98, the same $4 tax destroys ½ × $4 × 2 = $4 and raises $4 × 98 = $392. Identical tax, identical market size: ten times the waste in the first case and 22.5% more revenue in the second.
The comparison is sharper stated per dollar raised. That is 12.5 cents of surplus destroyed for every revenue dollar in the elastic market ($40 ÷ $320), against roughly 1 cent in the inelastic one ($4 ÷ $392). That ratio, rather than the raw triangle, is what makes one tax base cheaper to use than another.
One thing elasticity governs that this page deliberately does not report is incidence. The side less able to walk away absorbs the larger share of the wedge, so buyers and sellers rarely split the $320 evenly between them. The outputs here size the triangle and the transfer; they do not divide either one between the two sides of the market.
Doubling the tax to $8 does not double the $40 — it quadruples it
Raise the tax from $4 to $8 and the loss does not move from $40 to $80. Under the linear supply and demand this tool assumes, the quantity reduction is proportional to the wedge, so a tax that cost 20 units at $4 costs 40 units at $8. The triangle becomes ½ × $8 × 40 = $160 — four times the original, from a tax only twice as large.
Revenue does not keep pace. At $8 the surviving quantity is 60 and revenue is $8 × 60 = $480, up only half again from $320. Put the two together and the cost of collection jumps from 12.5 cents of destroyed surplus per revenue dollar ($40 ÷ $320) to about 33 cents ($160 ÷ $480). The second $4 of tax is far more expensive than the first, even though on paper the two look identical.
The triangle grows in two dimensions at once — taller because the wedge is bigger, wider because more trades become uneconomic — which is why its area moves roughly with the square of the rate. Two practical consequences follow. Intuition calibrated on a small levy badly understates the damage done by a steep one, and for a target amount of revenue a broad base at a low rate generally destroys less surplus than a narrow base at a high one. Both are visible here in a couple of keystrokes: change only the tax figure and watch the two outputs pull apart.
For a price ceiling or a monopoly, ignore the tax-revenue figure
Nothing in the arithmetic is specific to taxation. The formula needs a wedge and a quantity change, and plenty of things that are not taxes supply both. A binding price ceiling holds trade below the efficient quantity; so does a price floor, an import tariff, a quota, or a monopolist withholding output to lift price. In each case enter the wedge in the tax box and the two quantities as usual, and the deadweight loss and quantity reduction read correctly.
The tax revenue output is the one that stops being literal. It is really the wedge multiplied by the units that still trade, and who ends up holding that money changes with the mechanism. Under monopoly pricing it is producer profit. Under a quota it is rent to whoever holds the licences. Under a price ceiling a part of it is never collected by anyone at all, dissipating instead into queueing, shortage and search. Only when a government levies and collects the wedge is the label on that box accurate.
So read it as the size of the transfer rather than as government income, and answer the question of who pockets it separately. The triangle beside it is unaffected either way: surplus destroyed by a wedge is destroyed whoever imposed the wedge.
A pollution tax turns this triangle into a gain
Every number on this page rests on one unstated assumption: that the quantity traded before the wedge was the right quantity. If it was, removing trades destroys value and the triangle is a genuine cost. If it was not, the same arithmetic scores an improvement as a loss.
That is what happens whenever a market already misfires because the price ignores a cost borne by someone outside the trade — pollution, congestion, noise, strain on a shared resource. Left alone, such a market trades too much: the buyer and the seller are both better off at a quantity that makes third parties worse off. A tax set against that spillover pushes trade back toward the efficient level. The 20 units it removes were units society was losing on, and the $40 reported here is then not destroyed surplus at all.
The tool cannot tell the two situations apart. It sees a wedge and a fall in quantity, and it has no way of knowing whether 100 units was efficient or already too many. Settle that question before you read the output, and treat the figure as the cost of moving away from the pre-tax quantity — a real cost when that quantity was right, and a benefit wearing the wrong sign when it was not.
Three numbers cannot tell whether the tax caused the drop
The calculator attributes the entire fall from 100 units to 80 to the tax, because those three numbers are all it is given. Where the quantities come from different periods of real data, everything else that changed in between — incomes, input costs, the price of a substitute, a competitor entering, the weather — is silently loaded onto the wedge. No part of the arithmetic can separate a tax effect from a coincidence, and a triangle built on a badly attributed quantity change is precise about the wrong thing.
Several further gaps are worth stating plainly before the result is quoted anywhere.
None of this makes the number useless. It makes it a first-order estimate of one specific thing — the efficiency cost of trades a wedge prevented — which is exactly the job it is asked to do in policy work. Quote it with the assumptions it rests on attached, and it is honest; quote it bare, and it is not.
Curvature. With curved supply or demand the lost region is not exactly a triangle, so half the wedge times the quantity change is an approximation, and it drifts further from the truth the larger the wedge gets.
Administrative and compliance cost. The figure covers only the surplus lost to abandoned trades. Filing, collection, enforcement and the effort both sides spend navigating the rules all sit outside the model.
What the revenue buys. The $40 is calculated as though the $320 disappeared into a vault. Revenue spent on something worth more than it cost offsets the loss; revenue spent badly compounds it. This page scores one side of that ledger only.
Avoidance and relabelling. Trades that shift into an untaxed substitute, an informal market or another jurisdiction appear here purely as a larger quantity reduction, which is not always the same thing as surplus destroyed.
Distribution. A dollar of surplus counts the same whoever loses it. The triangle is silent on who bore the loss, and that is a separate judgement rather than a detail the model happens to omit.
Frequently Asked Questions
What is deadweight loss?
It is the value of mutually beneficial trades that no longer happen because a tax, subsidy, or other distortion has wedged price and quantity away from the efficient level. That lost surplus benefits no one — not buyers, sellers, or the government.
Why is deadweight loss a triangle?
The lost trades sit between the supply and demand curves over the range of quantity the tax wiped out. With linear curves that region is a right triangle whose height is the tax wedge and whose base is the drop in quantity.
How is deadweight loss different from tax revenue?
Tax revenue is money transferred from buyers and sellers to the government on the units still traded — it is not lost, just moved. Deadweight loss is surplus that vanishes entirely because those units stop trading.
How does elasticity affect deadweight loss?
The more responsive buyers or sellers are to price, the more the quantity falls for a given tax, widening the triangle. Taxes on elastic goods create larger deadweight losses than taxes on inelastic goods.
Who bears the deadweight loss?
It is shared by buyers and sellers as forgone consumer and producer surplus, but unlike tax revenue it is captured by no one. That is precisely why economists treat it as a pure efficiency cost.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.