π Deadweight Loss Calculator
The economic value a tax or subsidy destroys.
Deadweight loss (lost total surplus)
Estimates for planning only, not financial advice.
Deadweight loss is the economic value destroyed when a tax or subsidy stops mutually beneficial trades from happening. It is the triangle between the supply and demand curves: buyers who valued the good above its cost walk away because the tax pushed the price too high. The formula is one half times the per-unit tax times the drop in quantity. A $2 tax that cuts sales by 1,500 units destroys $1,500 of value that nobody collects, not the buyer, not the seller, and not the government.
How to Use This Calculator
Enter the tax per unit and the quantities traded before and after the tax. The calculator returns the deadweight loss triangle, the tax revenue raised, and the loss per dollar of revenue, which is the efficiency price of the tax.
Enter the per-unit tax, such as an excise tax per pack, per gallon, or per item.
Enter the quantity traded before the tax and the lower quantity after it. The gap between them drives the whole result.
Read the deadweight loss and compare it with revenue raised. A high loss per revenue dollar means an inefficient tax.
The Deadweight Loss Formula
The one-half is there because the loss is a triangle, not a rectangle: the first lost sale destroys almost the full tax wedge of value, the last lost sale destroys almost none. Two things grow the triangle fast. Bigger taxes grow it with the square of the tax, so doubling a tax roughly quadruples the loss. And more elastic markets, where buyers easily walk away, lose more quantity per dollar of tax and therefore more surplus.
Worked Example
A $2 per-unit tax cuts quantity from 10,000 to 8,500 units. Deadweight loss = 0.5 x $2 x 1,500 = $1,500. The tax raises $17,000 of revenue (8,500 x $2), so each revenue dollar costs about 8.8 cents of destroyed value. If the tax doubled to $4 and quantity fell to 7,000, the loss would quadruple to $6,000 while revenue only roughly doubles, which is why economists prefer broad, low-rate taxes over narrow, high-rate ones.
Reading Your Result
| Loss per revenue $1 | Interpretation |
|---|---|
| Under $0.10 | Relatively efficient tax, typical of broad bases |
| $0.10 to $0.30 | Material distortion, common for excise taxes |
| Above $0.30 | Heavily distorting, the tax base is eroding fast |
Common Mistakes
Forgetting the one-half is the classic slip; without it you are computing a rectangle, not the triangle. Using price change instead of the tax wedge also misleads when supply is not perfectly elastic. And remember this is a partial-equilibrium snapshot: it ignores where the revenue goes. A tax that funds something valuable can still be worth levying. To price the tax itself into a purchase decision, see our sales tax calculator, and for the business-side margin impact of cost shocks like this, our margin calculator keeps the arithmetic honest.
Deadweight Loss Beyond Taxes
The same triangle shows up wherever policy blocks willing trades. A price floor set above equilibrium, like an aggressive minimum price, creates a deadweight triangle from unsold surplus: producers want to sell more than buyers will take at that price. A quota does the same by capping quantity directly. In each case the formula keeps its shape, one half times the wedge times the quantity lost, which is why economists reach for it across so many policy debates.
Monopoly pricing creates a private-sector version. A monopolist restricts output to raise price, and the forgone trades form the same triangle, this time captured partly as profit rather than destroyed outright. Antitrust analysis weighs that triangle when judging mergers: if the deal raises prices and cuts output, the deadweight loss is part of the consumer harm. The geometry is identical; only who pockets the rectangle changes.
Who Really Bears the Tax
The deadweight triangle does not tell you who pays the tax, only how much value vanishes. Tax incidence, the split of the burden between buyers and sellers, depends on relative elasticity. When demand is inelastic and supply is elastic, buyers absorb most of the tax through higher prices; when the reverse holds, sellers absorb it through lower net receipts. The side that can walk away more easily pays less.
This is why taxing goods with few substitutes raises revenue with less political pain but not necessarily less distortion: the burden lands quietly on consumers who cannot adjust. Policymakers choosing between tax bases are really choosing whose behavior to distort and whose surplus to shrink. The triangle measures the cost; incidence decides who feels it. In practice, payroll taxes land mostly on workers through lower wages, while corporate taxes split between shareholders, workers, and customers depending on how mobile capital is. Either way, the triangle stays the same size; only the names on the lost surplus change.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is deadweight loss in simple terms?
Value destroyed when a tax stops trades that would have helped both buyer and seller. The buyer valued the good above its cost, the tax blocked the deal, and the lost surplus goes to nobody. It is pure waste from the marketβs point of view.
How do you calculate deadweight loss?
Multiply one-half by the per-unit tax by the fall in quantity: DWL = 1/2 x t x (Q1 - Q2). A $2 tax cutting sales by 1,500 units gives $1,500 of deadweight loss.
Why is deadweight loss a triangle?
Because the lost value shrinks sale by sale. The first unit priced out loses nearly the full tax wedge of surplus, while the last unit priced out loses almost none. Plotted on supply and demand, that gradient forms a triangle, hence the one-half.
Does deadweight loss grow with the tax rate?
Faster than the tax rate: it grows with the square of the tax. Doubling a tax roughly quadruples the deadweight loss, because both the wedge and the quantity lost double. This is the core argument for low, broad taxes.
Can a subsidy create deadweight loss?
Yes. A subsidy pushes quantity above the efficient level, funding trades that cost more than buyers value them at. The triangle appears on the other side, but the math is the same shape.
What is the difference between deadweight loss and tax revenue?
Tax revenue is the rectangle the government collects: tax times post-tax quantity. Deadweight loss is the triangle nobody collects. Together with consumer and producer surplus they account for the total pre-tax surplus.
Do all taxes create deadweight loss?
Nearly all taxes on transactions do, because they change behavior. Lump-sum taxes that do not depend on behavior create none in theory, but they are rarely practical. Land value taxes come closest in practice.
How does elasticity affect deadweight loss?
More elastic demand or supply means quantity reacts more to the tax, so the triangle gets wider and the loss bigger. Taxing goods people cannot easily give up, like gasoline short-term, creates less distortion per dollar raised.
Is deadweight loss the same as an economic loss?
It is a loss of total surplus, meaning buyers and sellers combined are worse off by that amount with no offsetting gain. Whether the tax is still worthwhile depends on what the revenue buys, which the triangle alone does not show.
Why do economists care about deadweight loss?
Because it measures the hidden cost of raising revenue. Two taxes can raise the same dollars with very different deadweight losses, and choosing the less distorting one leaves society richer by the difference.