Total utility from marginal utility: a running sum that peaks at 275, then the sixth slice drags it back to 270
To calculate total utility from marginal utility, add the marginal utility of every unit consumed so far: TU = MU₁ + MU₂ + … + MUₙ. Marginal utilities of 100, 80 and 55 give a total utility of 235 after three units. Going the other way, marginal utility is the difference between two consecutive totals.
Score six pizza slices at 100, 80, 55, 30, 10, −5 and the table returns total utility as a running sum — 100, 180, 235, 265, 275, 270 — with marginal utility equal to those per-unit scores. Marginal utility is the extra satisfaction from one more unit, MU = ΔTU ÷ ΔQ, the difference between two consecutive rows. Total utility is the satisfaction from every unit consumed so far, not just the latest one. Enter total utility instead and the calculator works backwards, taking the difference between consecutive rows.
The decision the table hands you sits in the sign of MU, not its size. While MU is positive, total utility keeps climbing; diminishing marginal utility begins at the second slice, where MU falls from 100 to 80. That is the law at work: as you consume more of one good, holding everything else equal, the marginal utility of each additional unit eventually declines. The satiation point is slice five — MU has run down to zero and total utility peaks at 275. Slice six carries a marginal utility of −5, so total utility falls to 270; consuming past satiation has a real cost, not merely a zero return.
The average-utility column (TU ÷ quantity) turns over as soon as marginal utility drops below the running average, which in this table is slice two as well. That downward-sloping MU curve — plotted here from your own values, with the satiation point marked and the zero crossing visible — is one reason demand curves slope down: each extra unit is worth less to you, so you will only take it at a lower price. Total utility and marginal utility move in opposite directions only once MU turns negative; before that, total utility rises the whole way while marginal utility falls.
How to calculate marginal utility per dollar: from ΔTU ÷ ΔQ to MU₁ ÷ P₁ = MU₂ ÷ P₂
Marginal utility per dollar is the marginal utility of the next unit divided by its price: MU ÷ P. A unit that adds 30 points of utility and costs $2 returns 15 per dollar; one that adds 24 at $3 returns 8. Spend the next dollar where the ratio is higher, and stop moving money once the ratios are equal across goods.
Four expressions generate every column below. In Function Presets mode the same four run against a textbook utility function — U(x) = √x, log, quadratic, or linear — instead of typed rows, computing total utility, marginal utility, and utility per dollar at each quantity directly from the function, so you can hold a curve you assumed against a table you actually scored.
When the good with the higher MU is the wrong home for your next dollar
Raw marginal utility ranks units inside one good; it cannot rank spending across goods, because the goods carry different prices. Utility per dollar = MU ÷ price is the column that can, and this calculator computes it for every row you enter. It measures satisfaction gained per unit of money spent, which is what you actually compare across goods when the budget is limited: of two goods at the same price, the one with the higher marginal utility per dollar is the better use of the next dollar — and a good with the lower marginal utility but the lower price can win outright.
Apply the rule repeatedly and it terminates in the equimarginal principle: keep moving the next dollar to whichever good returns the most utility per dollar, and stop when the ratio is level everywhere you spend — MU₁/P₁ = MU₂/P₂ = …, consumer equilibrium. That equality is the test the multi-good module runs when it allocates a budget across the goods and prices you list. Change one price and re-run: the two-scenario comparison shows the reordering directly, because a price rise cuts utility per dollar for that good while its marginal utility never moved.
The same column drives the suggested stopping point. Set a minimum utility per dollar and this calculator returns the last unit at or above it; leave it unset and the stop falls back to the unit before the first negative MU — slice five in the pizza table. A value-for-money floor can halt you well short of satiation.
When MRS equals the price ratio, there is nothing left to trade
The marginal rate of substitution is that same equilibrium seen from the trading side: MRS = MUX ÷ MUY, the units of good Y you would give up for one more unit of good X while total satisfaction stays unchanged. The MRS helper builds it from the utility scores you have already entered.
Set MRS against the price ratio and it becomes a stopping rule. MUX/PX = MUY/PY is the same statement as MRS = PX ÷ PY, so once what you are willing to trade matches what the market charges to trade, no further reshuffling of the basket raises total utility. Above that ratio, hold more X; below it, more Y.
Your scores are ordinal, so two goods compare only on one scale
The arithmetic here is exact; the inputs are opinions. That gap is the real limitation behind every number this tool returns, and it is why any comparison across goods needs one shared scale to mean anything.
Methodology
This calculator computes total utility, marginal utility, and utility per dollar from the scores and prices you enter, and identifies diminishing utility by comparing marginal utility across units. The on-page engine and the Excel workbook formulas are validated against hand-computed cases and an Excel-compatible formula engine on every change. Results reflect your own subjective scores.
- Utility is subjective and ordinal — the scores represent your own ranking, not a physical measurement in real units.
- Cross-good utility comparisons (multi-good module, MRS helper) are only meaningful when all scores use a consistent scale.
- The multi-good allocation follows a greedy equimarginal rule, which is an approximation — it does not account for income effects, substitute goods not listed, or diminishing MU that develops mid-allocation.
- Preferences change with mood, context, time, and habit — a single table is a snapshot, not a model of general behaviour.
- No live consumer data, empirical demand estimates, or professional economic, behavioural, or financial advice.
One distinction this tool does not make for you: diminishing marginal utility is about consumption — what an extra unit is worth to whoever consumes it — while diminishing returns is about production, the extra output an extra input buys. They share the word "diminishing" but describe different processes. For the production side, see the diminishing returns calculator.
Read the guide
There is no dedicated marginal-utility guide yet. The formula section above covers the equimarginal principle and MRS in full.