Deadweight Loss Calculator - Tax Triangle Estimate

Calculate deadweight loss from a tax or price control using the price change and quantity reduction. Measure efficiency cost before you intervene.

Enter the original equilibrium price and quantity, then the price and quantity after a tax or control, to estimate the efficiency triangle.

Deadweight loss = ½ × |P1 − P0| × |Q1 − Q0|

Initial Equilibrium Price (P0)

Initial Equilibrium Quantity (Q0)

New Price After Intervention (P1)

New Quantity After Intervention (Q1)

About the deadweight loss calculator

Deadweight loss is the surplus that disappears when a market is pushed away from the competitive quantity. A per-unit tax, a binding price ceiling, a price floor, or a quota can all create a wedge between the price buyers pay and the price sellers keep, and fewer units are traded. Those missing trades would have created value — buyer willingness above seller cost — that nobody captures. The deadweight loss calculator estimates that lost triangle from two prices and two quantities. Under linear supply and demand, the efficiency loss is the area of a triangle: ½ × |price change| × |quantity change|. If the market moves from $10 and 100 units to $12 and 80 units, the price gap is $2 and 20 units are no longer traded, so deadweight loss is ½ × 2 × 20 = $20. A price rise from $5 to $8 with quantity falling from 200 to 150 produces ½ × 3 × 50 = $75. The same formula applies when a ceiling cuts the price and quantity still falls because suppliers withdraw: ½ × |ΔP| × |ΔQ|. Policy analysts use the triangle as a first-pass cost of a tax or control before turning to elasticities, distribution, and administration. It is not the tax revenue. Revenue is the rectangle of the tax wedge times the units still sold; deadweight loss is the extra surplus destroyed on units that are no longer sold. A small tax on an inelastic good can raise a lot of revenue with little deadweight loss; a large tax on an elastic good does the reverse. The linear-triangle shortcut assumes you can observe (or assume) both the pre- and post-intervention equilibria. Real demand and supply curves are not always straight, and quantity may change for reasons other than the policy — income, costs, or seasonality. If you only know elasticities, you would estimate ΔQ from those elasticities rather than treating Q1 as given. Externalities also matter: a tax that corrects pollution can reduce a negative externality even while creating a textbook triangle on the private market. Use the deadweight loss calculator to size a proposed tax, a minimum wage that reduces hours, or a rent control that shrinks the rental stock, then stress-test the quantity change. Recalculate when either the price wedge or the missing quantity is revised. The estimate is in the same currency units as the prices you enter and does not include compliance costs, lobbying, or transfers. Keep those caveats next to the number when you present it.

Deadweight loss examples

Each result is ½ × the absolute price change × the absolute quantity change.

Inputs	Deadweight loss	Note
P0 $10; Q0 100; P1 $12; Q1 80	$20.00	A $2 tax wedge and 20 lost units produce a $20 triangle.
P0 $5; Q0 200; P1 $8; Q1 150	$75.00	Price rises $3 and quantity falls 50, so ½ × 3 × 50 = $75.
P0 $20; Q0 80; P1 $15; Q1 60	$50.00	A $5 price drop with 20 fewer units still yields ½ × 5 × 20 = $50.

How to calculate deadweight loss

Enter the competitive or pre-policy equilibrium price and quantity (P0 and Q0).
Enter the price and quantity after the tax, ceiling, floor, or quota (P1 and Q1).
Select Calculate Deadweight Loss to see the triangle ½ × |ΔP| × |ΔQ|.
Compare alternative quantity responses if the size of the market reaction is uncertain.

Deadweight loss FAQ

What is the deadweight loss formula for a tax?

With linear curves, deadweight loss equals ½ × the tax wedge (or price gap) × the reduction in quantity. That is the surplus on trades that no longer happen, not the revenue the government collects.

Is deadweight loss the same as tax revenue?

No. Tax revenue is the rectangle of the per-unit tax times units still sold. Deadweight loss is the triangle on units that disappear. Both can exist at once.

Does the formula work for price ceilings and floors?

Yes, as a first approximation, if you can measure how much price and quantity moved. A ceiling that does not bind, or a floor below equilibrium, produces no triangle because quantity does not change.

Why take absolute values of the changes?

Price may rise (a tax on buyers) or fall (a ceiling). Quantity almost always falls when the control binds. Absolute values keep the triangle area positive in either direction.

When is the triangle a poor estimate?

When curves are highly nonlinear, when quantity changed for reasons other than the policy, or when externalities mean the competitive quantity was not efficient to begin with. Use it as a transparent starting point.