How to Calculate Real Exchange Rate Using Cpi

Real Exchange Rate Calculator (CPI Method)

Units of Domestic Currency per 1 Unit of Foreign Currency (Direct Quote)

Current price index of your home country

Current price index of the foreign country

function calculateRER() { // Get inputs by exact ID var nominal = parseFloat(document.getElementById('nominalRate').value); var domesticPrice = parseFloat(document.getElementById('domesticCPI').value); var foreignPrice = parseFloat(document.getElementById('foreignCPI').value); var resultDiv = document.getElementById('resultOutput'); var resultValueDiv = document.getElementById('rerResult'); var explanationDiv = document.getElementById('rerExplanation'); // Reset display resultDiv.style.display = 'none'; // Validation if (isNaN(nominal) || isNaN(domesticPrice) || isNaN(foreignPrice)) { alert("Please enter valid numeric values for all fields."); return; } if (domesticPrice === 0) { alert("Domestic CPI cannot be zero."); return; } // Calculation Logic: RER = Nominal Rate * (Foreign CPI / Domestic CPI) // This assumes Nominal Rate is quoted as Domestic/Foreign. var rer = nominal * (foreignPrice / domesticPrice); // Analysis text var analysisText = ""; var purchasingPower = ""; if (rer > nominal) { analysisText = "The Real Exchange Rate (" + rer.toFixed(4) + ") is higher than the Nominal Rate (" + nominal + ")."; purchasingPower = "This implies the foreign country's price level is higher relative to the domestic price level (adjusted for currency). Foreign goods are relatively expensive compared to domestic goods."; } else if (rer < nominal) { analysisText = "The Real Exchange Rate (" + rer.toFixed(4) + ") is lower than the Nominal Rate (" + nominal + ")."; purchasingPower = "This implies domestic goods are relatively expensive compared to foreign goods when adjusted for price levels."; } else { analysisText = "The Real Exchange Rate equals the Nominal Rate."; purchasingPower = "Price levels are at parity relative to the exchange rate."; } // Display Results resultValueDiv.innerHTML = "Real Exchange Rate: " + rer.toFixed(4); explanationDiv.innerHTML = "Interpretation: " + analysisText + "" + purchasingPower; resultDiv.style.display = 'block'; }

The Real Exchange Rate (RER) is a crucial economic indicator that compares the relative price of goods between two countries. Unlike the nominal exchange rate—which simply tells you how much one currency is worth in terms of another—the real exchange rate adjusts for the differences in price levels (inflation) between those countries.

Economists and investors use the RER to determine the true purchasing power of a currency and to assess the international competitiveness of a country's tradeable goods.

The Real Exchange Rate Formula

To calculate the Real Exchange Rate using the Consumer Price Index (CPI), we use the following standard formula:

RER = e × (P* / P)

Where:

• e (Nominal Exchange Rate): The current market exchange rate, defined as units of Domestic Currency per 1 Unit of Foreign Currency.
• P* (Foreign CPI): The price level or Consumer Price Index of the foreign country.
• P (Domestic CPI): The price level or Consumer Price Index of the domestic country.

Step-by-Step Calculation Example

Let's walk through a practical example to understand how the numbers interact.

Scenario: You are in the United States (Domestic) analyzing trade with the Eurozone (Foreign).

• Nominal Exchange Rate ($e$): 1.10 (Assume $1.10 USD buys 1 Euro).
• Domestic CPI ($P$): 120 (Price level in the US).
• Foreign CPI ($P^*$): 115 (Price level in the Eurozone).

The Calculation:

1. Divide the Foreign CPI by the Domestic CPI:

115 / 120 = 0.9583

2. Multiply this ratio by the Nominal Exchange Rate:

1.10 × 0.9583 = 1.0541

Result: The Real Exchange Rate is approximately 1.05. Because the RER (1.05) is lower than the nominal rate (1.10), it suggests that goods in the US are relatively more expensive than the underlying exchange rate suggests, or conversely, Eurozone goods are cheaper in real terms.

Why Use CPI in Exchange Rates?

The Nominal Exchange Rate is often volatile and determined by currency market speculation. However, it does not account for inflation. If a country has high inflation, its goods become more expensive. If the currency doesn't depreciate to match that inflation, the country loses competitiveness.

By using the Consumer Price Index (CPI) as a proxy for price levels ($P$ and $P^*$), the RER formula strips away the effects of inflation to reveal the "real" economic relationship between two currencies. This is closely related to the theory of Purchasing Power Parity (PPP).

Interpreting the Results

• RER Increases (Real Depreciation): If the RER rises, foreign goods become relatively more expensive compared to domestic goods. This generally boosts the domestic country's exports because they appear cheaper to foreigners.
• RER Decreases (Real Appreciation): If the RER falls, foreign goods become relatively cheaper. This encourages imports but hurts domestic exporters, as their goods become more expensive for foreign buyers.
• RER = 1 (or constant): If the RER remains constant over time, Purchasing Power Parity holds, meaning inflation differentials are being perfectly offset by changes in the nominal exchange rate.

Common Pitfalls

When using this calculator, ensure you are using the correct quoting convention for the Nominal Exchange Rate. This tool assumes a "Direct Quote" (Domestic Currency / Foreign Currency). If you have an "Indirect Quote" (Foreign Currency / Domestic Currency), you must either invert the rate (1 / rate) or flip the CPI fraction (Domestic CPI / Foreign CPI) in your manual calculations.