Foreign Currency per unit of Domestic Currency (e.g., $1.20 Foreign per $1 Domestic)
Consumer Price Index (CPI) or cost of basket in home country
Consumer Price Index (CPI) or cost of basket in foreign country
Real Exchange Rate (RER)
0.0000
function calculateRER() {
// Get input values
var nominal = document.getElementById('nominalRate').value;
var domesticP = document.getElementById('domesticPrice').value;
var foreignP = document.getElementById('foreignPrice').value;
// Parse inputs
var e = parseFloat(nominal);
var p = parseFloat(domesticP);
var pStar = parseFloat(foreignP);
// Validation
if (isNaN(e) || isNaN(p) || isNaN(pStar) || e < 0 || p <= 0 || pStar e) {
text = "The Real Exchange Rate (" + realRate.toFixed(4) + ") is higher than the Nominal Rate (" + e + "). This implies that the domestic price level is higher relative to the foreign price level compared to the nominal exchange conversion. Domestic goods are relatively more expensive than foreign goods.";
} else if (realRate < e) {
text = "The Real Exchange Rate (" + realRate.toFixed(4) + ") is lower than the Nominal Rate (" + e + "). This implies that the domestic price level is lower relative to the foreign price level. Domestic goods are relatively cheaper, potentially increasing export competitiveness.";
} else {
text = "The Real Exchange Rate equals the Nominal Rate, implying equal relative price levels (Purchasing Power Parity holds exactly relative to the indices used).";
}
explanationDisplay.innerHTML = text;
}
How to Calculate Real Exchange Rate from Nominal
The Real Exchange Rate (RER) is a crucial concept in international economics that adjusts the nominal exchange rate by the relative price levels (usually measured by the Consumer Price Index, or CPI) between two countries. While the nominal exchange rate tells you how much foreign currency you can buy with a unit of domestic currency, the real exchange rate tells you what that currency can actually buy in terms of goods and services.
Understanding the RER allows economists, investors, and policymakers to determine the true competitiveness of a nation's trade and whether a currency is overvalued or undervalued relative to purchasing power parity.
The Real Exchange Rate Formula
To calculate the Real Exchange Rate from the Nominal Exchange Rate, you need three specific variables: the nominal rate itself, the domestic price level, and the foreign price level. The standard formula is:
RER = e × (P / P*)
Where:
RER = Real Exchange Rate
e = Nominal Exchange Rate (defined as Foreign Currency per unit of Domestic Currency)
P = Domestic Price Level (e.g., Domestic CPI)
P* = Foreign Price Level (e.g., Foreign CPI)
Step-by-Step Calculation Guide
Follow these steps to perform the calculation manually or using the calculator above:
1. Identify the Nominal Rate
Find the current market exchange rate. Ensure it is quoted as "Foreign Currency per Domestic Currency." For example, if you are in the US (Domestic) and looking at Europe (Foreign), use the rate USD/EUR (e.g., 0.85 Euros per 1 Dollar).
2. Determine Price Levels
Obtain the price indices for both countries. The Consumer Price Index (CPI) is the most common metric. Ensure both indices are based on the same base year for accuracy (e.g., 2010=100).
3. Apply the Math
Multiply the Nominal Rate by the ratio of Domestic Price to Foreign Price.
Example:
Nominal Rate ($e$): 1.50 (1 Unit Domestic = 1.50 Units Foreign)
In this example, the Real Exchange Rate is roughly 1.64. Because the RER is higher than the nominal rate, domestic goods are relatively more expensive than foreign goods once adjusted for currency conversion.
Why the Real Exchange Rate Matters
Trade Competitiveness: If the real exchange rate rises (appreciates), domestic goods become more expensive for foreigners, which can reduce exports. Conversely, if the RER falls (depreciates), domestic goods become cheaper, potentially boosting exports.
Purchasing Power: The RER helps compare the standard of living. It reflects the quantity of a foreign basket of goods that can be exchanged for one domestic basket of goods.
Interpretation of Results
RER = 1: Purchasing Power Parity (PPP) holds. One unit of currency buys the same amount of goods in both countries.
RER > 1: The domestic currency is "overvalued" in real terms. It is cheaper to buy goods abroad than at home.
RER < 1: The domestic currency is "undervalued" in real terms. Domestic goods are cheaper compared to foreign equivalents.