The real exchange rate and the home currency’s gap to purchasing-power parity if the nominal rate moved, with both prices unchanged. In change mode, the real change at other inflation gaps.
Nominal rate or inflation gap
Real rate or real change
Home currency against PPP
90
1.125
+12.5%
120
1.500
+50.0%
150
1.875
+87.5%
◀ yours
180
2.250
+125.0%
80
1.000
0.0%
◀ PPP
Calculated in your browser — the numbers you enter are never sent to our servers.
What it calculates: Real exchange rate (ε), Purchasing-power-parity rate, Home currency against PPP, Foreign currency against PPP.
Updated 22 September 2026 · Transparent assumptions
At ¥150 per dollar, a $6.00 burger is worth ¥900 against a ¥480 local price: a real rate of 1.875
The nominal exchange rate says how many yen a dollar buys. The real exchange rate says how many Japanese goods one US good buys: convert the US price into yen at the nominal rate and divide by the Japanese price. With the dollar at ¥150, a $6.00 burger costs ¥900 in yen terms against ¥480 for the same burger in Tokyo, so ε = 900 ÷ 480 = 1.875.
ε = e × P ÷ P*
A real rate above 1 means home goods are dear relative to foreign goods at today’s nominal rate; below 1, cheap. The calculator accepts the nominal rate either way round — ¥ per $ or $ per € — and inverts it when needed.
Worked example
e = 150, P = 6.00, P* = 480
ε = 150 × 6.00 ÷ 480
ε = 1.875
Purchasing-power parity puts the rate at ¥80 per dollar, so the yen looks 46.7% undervalued
Purchasing-power parity says that in the long run exchange rates should move to make the same good cost the same everywhere: ε = 1. The PPP rate is the nominal rate that achieves it, P* ÷ P = 480 ÷ 6.00 = ¥80 per dollar. At the actual ¥150, the dollar buys 87.5% more than parity and the yen 46.7% less.
PPP rate = P* ÷ P
The Economist has published this comparison for the Big Mac since 1986 as a light-hearted test of PPP. It is useful for intuition and a poor guide to where currencies will go, for the reasons in the next section.
Against parity
PPP = 480 ÷ 6.00 = 80
dollar: 150 ÷ 80 − 1 = +87.5%
yen: 80 ÷ 150 − 1 = −46.7%
Rent, wages and taxes keep a burger’s price local, which is why PPP fails for years at a time
Much of a burger’s price is rent, local wages and sales tax — none of which can be traded across borders — so arbitrage cannot close the gap. Transport costs, tariffs and brand pricing add more. Richer countries also tend to have higher prices for non-traded services, because their productivity in traded goods raises wages across the economy: the Balassa–Samuelson effect.
For those reasons real exchange rates can stay far from 1 for decades. PPP-based comparisons of living standards, such as the World Bank’s, use broad baskets precisely to avoid reading too much into one good.
With the nominal rate unchanged, 3% inflation at home against 1% abroad is a real appreciation of 1.98%
Over time the real rate moves with the nominal rate and with relative inflation: real change = (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.
Δε = (e₁ ÷ e₀) × (1 + π) ÷ (1 + π*) − 1
Choose change mode to run this with your own rates and inflation. A country with persistently higher inflation must see its currency depreciate nominally just to keep its real rate — and its exporters’ competitiveness — where it was.
A real appreciation
e₁ ÷ e₀ = 150 ÷ 150 = 1
1 × 1.03 ÷ 1.01 − 1
= +1.98%
A higher real exchange rate makes exports dearer abroad and imports cheaper at home
Buyers respond to relative prices, so it is the real rate, not the nominal one, that drives trade. When ε rises, a country’s goods cost more in foreign terms and foreign goods 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, so the trade balance often worsens before improving — the J-curve.
The BIS real broad index for the dollar stood at 108.25 in July 2026, with 2020 = 100
For policy, economists use real effective exchange rates: the real rate against many trading partners at once, weighted by trade, and built from price indices rather than price levels. The Bank for International Settlements publishes one for about 60 economies; its real broad index for the US dollar read 108.25 in July 2026 against 100 in 2020, meaning US goods had become about 8% dearer relative to its partners’ goods since 2020.
Because they use indices, these series measure changes, not levels: an index of 108 does not say the dollar is 8% overvalued, only that it is 8% stronger in real terms than in the base year.
EUR/USD 1.08 means dollars per euro, so the formula needs its inverse for a US home currency
The commonest mistake is using the rate the wrong way round.
Currency pairs quote the second currency per unit of the first: EUR/USD 1.08 is 1.08 dollars per euro; USD/JPY 150 is 150 yen per dollar.
The formula uses foreign currency per unit of home currency. For a US home currency, USD/JPY 150 goes in as it is; EUR/USD 1.08 must be inverted to 0.926 euros per dollar — choose “home currency per 1 foreign” and the calculator does it.
Prices must be for the same good. A burger against a burger, or a basket against the same basket — never an index against a price.
Frequently Asked Questions
What is the formula for the real exchange rate?
ε = e × P ÷ P*, where e is the nominal rate in foreign currency per unit of home currency, P is the home price and P* the foreign price of the same good or basket.
What is the difference between the nominal and real exchange rate?
The nominal rate is the price of one currency in another. The real rate is the price of one country’s goods in terms of another’s, which also depends on the price levels in both.
What does a real exchange rate above 1 mean?
Home goods cost more than the same foreign goods after converting at the nominal rate. By purchasing-power parity the home currency is overvalued.
Can a currency appreciate in real terms without its exchange rate changing?
Yes. If home inflation exceeds foreign inflation while the nominal rate stays put, home goods become relatively dearer — a real appreciation.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
Sudha, J. (2026, September 22). Real Exchange Rate Calculator. Calculator Matters. https://calculatormatters.com/economics/real-exchange-rate-calculator/
The Real Exchange Rate and Purchasing Power Parity
What a currency buys in goods: the real exchange rate e × P ÷ P*, the PPP rate, over- and undervaluation, and why prices do not equalise, using a burger.