The deadweight loss calculator above takes a linear demand curve, a linear supply curve and one of five interventions, all supplied by you, and returns the deadweight loss triangle together with the quantity traded, the price buyers pay, the price sellers keep, the revenue raised or subsidy paid, and how the burden divides between the two sides.
Deadweight loss is a model output, not a measurement. It is the value of the mutually beneficial trades that stop happening because an intervention has moved the traded quantity away from where marginal benefit equals marginal cost. Arb Digital publishes this page with every parameter as an input and no economic data of any kind, because a hard-coded elasticity would be stale within a quarter and wrong for your market anyway. For the surplus areas themselves, our consumer surplus calculator uses the same curve convention.
What This Deadweight Loss Calculator Does
It first solves the competitive benchmark. With demand P = a − bQ and supply P = c + dQ, the two curves cross at Q* = (a − c) ÷ (b + d), and that quantity is the point where the last unit traded is worth exactly what it cost to make. Every intervention is then measured as a departure from it.
Five interventions are handled. A per-unit tax drives a wedge between the buyer's price and the seller's, shrinking the quantity. A per-unit subsidy does the reverse, pushing quantity above the benchmark so that units get made which cost more than they are worth. A price floor above the benchmark cuts quantity to what buyers will take at that price. A price ceiling below it cuts quantity to what sellers will offer. A quantity cap restricts trade directly.
In every case the tool reports the resulting quantity, both prices, the transfer to or from government where one exists, and the triangle. It also reports the statutory-versus-economic split, because the side that legally pays a tax is almost never the side that bears it.
Where an intervention is not binding — a floor set below the market price, a cap set above the market quantity — the tool says so in words and reports a loss of zero rather than a meaningless number. That case is worth seeing, because a great many real price controls are non-binding for long stretches.
How to Use It
- Enter your four curve coefficients. Both slopes must be positive and the demand intercept must exceed the supply intercept, or no trade occurs at all.
- Pick the intervention from the five available, matching how the policy you are modelling actually works.
- Enter its size — a money amount per unit for a tax or subsidy, a price for a control, a quantity for a cap.
- Read the hero for the triangle, and the grid for quantity, both prices and the government transfer.
- Check the incidence panel to see which side actually bears the burden, and the working panel to reproduce the arithmetic.
The Formula and How It Is Calculated
All five cases reduce to one expression. If the intervention moves the traded quantity from Q* to Q, the lost surplus is the area between the demand and supply curves over the missing range, and for linear curves that is:
DWL = ½ (b + d) (Q* − Q)²
The vertical gap between the two curves at any quantity is (a − c) − (b + d)Q, which is zero at Q* and widens linearly as you move away. Integrating that gap over the missing units gives the triangle. The same formula covers over-production under a subsidy, where the gap is negative and the squared term makes the loss positive again.
For a per-unit tax t the quantity becomes Q = (a − c − t) ÷ (b + d), so Q* − Q = t ÷ (b + d) and the loss simplifies to t² ÷ (2(b + d)). The burden split follows from the slopes alone: buyers bear d ÷ (b + d) of the tax and sellers bear b ÷ (b + d), regardless of who writes the cheque.
Work the default values through by hand. With a = 100, b = 1, c = 20, d = 1 and a tax of 10, the untaxed equilibrium is Q* = 40 at a price of 60. With the tax, Q = (100 − 20 − 10) ÷ 2 = 35. Buyers pay 100 − 35 = 65 and sellers keep 65 − 10 = 55. Revenue is 10 × 35 = 350. The deadweight loss is ½ × 2 × 5² = 25, which matches t² ÷ (2(b + d)) = 100 ÷ 4 = 25. Buyers bear 5 of the 10, exactly half, because the two slopes are equal.
Why the Loss Grows With the Square
This is the single most useful thing on the page. The triangle is proportional to the square of the tax, while the revenue is roughly proportional to the tax itself. Double a small tax and revenue not quite doubles, while the excess burden quadruples.
The consequences run in both directions. A small tax on a large base is very cheap in efficiency terms — the triangle on a tiny wedge is second-order small, which is the standard argument for broad, low-rate taxes over narrow, high-rate ones. And a tax that is already high is expensive to raise further, because you are adding to the widest part of the triangle. The U.S. Treasury's Office of Tax Analysis publishes the technical work behind revenue and burden estimates built on exactly this framework.
Run the tool at 10, then 20, then 40 with the default curves and watch it: 25, then 100, then 400, while revenue goes 350, 600, then 800 before starting to fall. That turning point is the revenue-maximising rate, and it is nowhere near the efficiency-maximising one.
Who Actually Bears the Burden
The legal incidence of a tax and its economic incidence are different things, and the model makes the gap explicit. Whether a tax is collected from sellers or buyers, the quantity, the two prices and the triangle come out identical. Only the labels change.
What determines the split is relative elasticity. The less responsive side bears more, because it has fewer alternatives. If demand is nearly vertical — a large b relative to d — buyers absorb almost the whole tax. If supply is nearly vertical, sellers do. In the limit where one side is perfectly inelastic, that side bears the entire burden and there is no deadweight loss at all, because the quantity does not move. That is the theoretical case for taxing genuinely fixed factors such as land.
The incidence panel reports the split as a percentage so you can see it move as you change the slopes. Our price elasticity calculator converts observed price and quantity pairs into the elasticities those slopes represent, and our sales tax calculator handles the arithmetic of an actual rate applied to an actual price.
What the Triangle Leaves Out
Deadweight loss is a partial equilibrium measure of one market in isolation, and there are at least four things it does not capture. Stating them matters, because the number is often quoted as if it were the whole cost of a policy.
It ignores administrative and compliance costs, which for some taxes exceed the triangle. It ignores externalities: where a good imposes uncompensated costs on third parties, the competitive quantity is not the efficient one, and a corrective tax reduces the true social loss while this model shows it increasing. It ignores distribution entirely, adding every party's gain and loss at equal weight. And it assumes competition; under market power the untaxed quantity is already below the efficient level, so the benchmark itself is wrong.
It also assumes the revenue simply vanishes from the analysis as a transfer. In reality that money funds something, and comparing a tax's excess burden against zero rather than against the value of what it pays for is a category error. Research on how these estimates are actually built is published in the Federal Reserve Board's Finance and Economics Discussion Series, and the underlying national accounts conventions are documented in the U.S. Bureau of Economic Analysis methodologies. Use your own country's statistics office if you are working elsewhere.
Arb Digital builds free tools that say where the answer stops being reliable instead of quietly rounding it off.
Browse All Free Tools Talk To Our TeamCommon Mistakes to Avoid
- Scaling the loss linearly with the tax — it grows with the square, so intuition calibrated on small taxes badly understates the cost of large ones.
- Assuming the side that remits the tax bears it — statutory incidence has no effect on the outcome; only relative elasticity determines the split.
- Treating a subsidy as costless — it produces a triangle too, because units get made whose cost exceeds what buyers value them at.
- Applying the model to a market with externalities — there the untaxed equilibrium is not efficient, so the triangle is measured from the wrong benchmark.
- Quoting the triangle as the total cost of a policy — it excludes compliance costs, distribution, and the value of whatever the revenue funds.
Related Free Tools From Arb Digital
Compute the surplus areas themselves with the consumer surplus calculator, turn observed prices and quantities into elasticities with the price elasticity calculator, apply a real rate to a real price with the sales tax calculator or the VAT calculator, or work out the cost of the next unit with the marginal cost calculator. The full free online tools hub lists every economics tool we publish.
Frequently Asked Questions
It is the value of the mutually beneficial trades that no longer happen because an intervention has moved the traded quantity away from the point where marginal benefit equals marginal cost.
Because both the number of lost units and the value of each lost unit rise in proportion to the tax, and the triangle multiplies the two. Doubling a tax therefore roughly quadruples the loss.
No. The quantity, both prices and the triangle are identical whether the tax is collected from buyers or from sellers. Only the relative elasticities determine who actually bears it.
Yes. It pushes quantity above the competitive level, so units get produced whose cost of production exceeds what buyers value them at, and that excess is the triangle.
Because any figure we published would be stale within a quarter and wrong for your market. Every coefficient is your input, taken from a source you can cite.
Nothing. It is not binding, the market clears at the equilibrium price, and the deadweight loss is zero. The tool says so rather than returning a meaningless figure.
No. It excludes administrative and compliance costs, ignores distribution entirely, and treats the revenue as a pure transfer rather than money that funds something of value.
Whenever the market has externalities or significant market power. In those cases the untaxed quantity is not the efficient one, so distance from it does not measure a welfare loss.
This page explains a standard microeconomic model for educational purposes and is not tax, investment or policy advice. It publishes no economic data; every parameter is your own input, and the result is only as sound as the curves you supply.
