Nominal rates price currencies; real rates price goods
Suppose a burger costs $6.00 in the United States and ¥480 in Japan, and the dollar buys ¥150. Converted at that rate, the US burger costs ¥900 — nearly twice the Japanese price. The real exchange rate states that ratio directly: ε = e × P ÷ P* = 150 × 6.00 ÷ 480 = 1.875.
Read it as one US burger trades for 1.875 Japanese burgers. A real rate above 1 means home goods are dear relative to foreign goods at today's nominal rate; below 1, cheap.
Worked example
e = 150 ¥ per $, P = $6.00, P* = ¥480
ε = 150 × 6.00 ÷ 480
ε = 1.875
Purchasing-power parity: the rate that would equalise prices
Purchasing-power parity says that in the long run the nominal rate should adjust until the same good costs the same everywhere, so that ε = 1. The rate that achieves it — the PPP rate — is P* ÷ P = 480 ÷ 6.00 = ¥80 per dollar.
Against that benchmark, the actual ¥150 makes the dollar 87.5% overvalued and the yen 46.7% undervalued. The Economist has published this burger comparison since 1986 as its Big Mac index — a light-hearted test of PPP rather than a forecast.
Worked example
PPP = 480 ÷ 6.00 = ¥80 per $
Dollar: 150 ÷ 80 − 1 = +87.5%
Yen: 80 ÷ 150 − 1 = −46.7%
Why prices do not equalise
Much of a burger's price is rent, local wages and sales tax — none of which can be shipped across a border — so no trader can buy burgers cheaply in Tokyo and sell them in New York. Transport costs, tariffs and brand pricing widen the gap further.
There is also a systematic pattern: richer countries tend to have higher prices for services that are not traded. Their productivity in traded goods lifts wages across the economy, including in haircuts and restaurants — the Balassa–Samuelson effect. A currency whose real rate is above 1 is due to fall. Real rates can stay far from 1 for decades.
A real appreciation with an unchanged exchange rate
Over time the real rate moves with the nominal rate and with relative inflation: the real change is (e₁ ÷ e₀) × (1 + π) ÷ (1 + π*) − 1. If the dollar stays at ¥150 but US prices rise 3% while Japanese prices rise 1%, US goods become 1.03 ÷ 1.01 − 1 = 1.98% dearer relative to Japanese goods.
The dollar has appreciated in real terms although its nominal price never moved. A country with persistently higher inflation must see its currency depreciate nominally just to stand still in real terms — which is why high-inflation currencies tend to weaken year after year.
Worked example
e₁ = e₀ = 150, π = 3%, π* = 1%
1 × 1.03 ÷ 1.01 − 1
= +1.98%
The real rate moves the trade balance
Buyers respond to relative prices, so trade follows the real rate. When ε rises, a country's goods cost more abroad and imports cost less at home; exports fall, imports rise and net exports decline. When ε falls, the reverse.
The response is slow. After a depreciation, import bills rise at once while quantities take months to adjust as buyers switch suppliers, so the trade balance often worsens before it improves — the J-curve.
Trade-weighted real rates, and a quoting trap
Policy work uses real effective exchange rates: the real rate against many partners at once, weighted by trade and built from price indices. The Bank for International Settlements' real broad index for the US dollar read 108.25 in July 2026 against 100 in 2020 — US goods about 8% dearer relative to partners' goods than in 2020. Because these indices use price indices, not price levels, they measure changes, not over- or undervaluation.
One trap catches almost everyone: currency pairs quote the second currency per unit of the first. USD/JPY 150 is ¥150 per dollar, but EUR/USD 1.08 is $1.08 per euro. For a US home currency the formula needs foreign currency per dollar, so EUR/USD must be inverted to 0.926 euros per dollar. The real exchange rate calculator accepts either convention and inverts when needed.
Common mistakes
Using the rate the wrong way round.The formula needs foreign currency per unit of home currency; invert pairs such as EUR/USD first.Comparing different goods.The two prices must be for the same good or the same basket, never an index against a price.Treating PPP as a forecast.Real rates can stay far from parity for years because of non-traded costs, taxes and productivity differences.Reading an index level as a valuation.A real effective rate of 108 says the currency is 8% stronger than in the base year, not that it is 8% overvalued.