How to Calculate Real Exchange Rate Formula

Real Exchange Rate (RER) Calculator

Units of Foreign Currency per 1 Unit of Domestic Currency

Economic Implication:

Economic Implication:

Understanding the value of money across borders requires more than just looking at the currency exchange board at an airport. To truly grasp the purchasing power and economic competitiveness of a nation, economists rely on the Real Exchange Rate (RER). This guide explains how to calculate the real exchange rate formula and why it is a critical metric in international macroeconomics.

What is the Real Exchange Rate?

The Nominal Exchange Rate is the price of one currency in terms of another (e.g., how many Euros you get for one US Dollar). However, this rate does not account for the differences in the cost of living or inflation between two countries.

The Real Exchange Rate (RER) adjusts the nominal rate by the ratio of the domestic price level to the foreign price level. It effectively measures the quantity of foreign goods required to purchase one unit of domestic goods.

The RER Formula

To calculate the Real Exchange Rate, you need three variables:

1. Nominal Exchange Rate ($e$): Typically defined as units of foreign currency per unit of domestic currency.
2. Domestic Price Level ($P$): Often represented by the Consumer Price Index (CPI) of the home country.
3. Foreign Price Level ($P^*$): The CPI of the foreign country.

$$RER = e \times \frac{P}{P^*}$$

Where:

• $e$ = Nominal Exchange Rate
• $P$ = Domestic Price Level
• $P^*$ = Foreign Price Level

Step-by-Step Calculation Example

Let's assume we are calculating the RER for the United States (Domestic) versus the Eurozone (Foreign).

• Nominal Rate ($e$): 0.85 Euros per 1 USD.
• US Price Level ($P$): 120 (CPI Index).
• Eurozone Price Level ($P^*$): 110 (CPI Index).

Using the formula:

$$RER = 0.85 \times \frac{120}{110}$$
$$RER = 0.85 \times 1.0909$$
$$RER \approx 0.9273$$

In this example, the real exchange rate is approximately 0.9273. Since the RER (0.9273) is higher than the nominal rate (0.85), it indicates that the US price level is higher relative to the Eurozone, making US goods effectively more expensive in real terms.

Why is RER Important?

Calculating the real exchange rate provides insights that the nominal rate hides:

• Competitiveness: An increase in RER (Real Appreciation) means domestic goods are becoming more expensive relative to foreign goods, potentially hurting exports.
• Standard of Living: A higher RER can also imply that domestic residents can purchase more foreign goods for the same amount of domestic labor (increased purchasing power).
• Inflation Adjustments: If a country has high inflation but the nominal exchange rate stays flat, the RER will rise, indicating a loss of trade competitiveness.

Interpreting the Results

When using the calculator above:

• If RER = 1: Purchasing Power Parity (PPP) holds; the cost of a basket of goods is the same in both countries when converted to a common currency.
• If RER > 1: Domestic goods are more expensive than foreign goods.
• If RER < 1: Domestic goods are cheaper than foreign goods.