Currency & Forex

Exchange-rate conversion, cross rates, spreads, pips and purchasing-power measures used in foreign exchange

Currency & Forex formulas help you convert between currencies, compare exchange rates, and understand how prices move in the foreign exchange market. They’re useful for students, exam prep, and anyone working with travel money, international business, trading, or economics, because these calculations reveal true value, market spreads, and whether exchange rates create opportunities or risks.

Currency Conversion

Foreign = Domestic \times Rate

Convert an amount from one currency to another using the quoted exchange rate.

Inverse Exchange Rate

Rate_{B/A} = \dfrac{1}{Rate_{A/B}}

Flip a quoted rate to express it from the other currency’s point of view.

Currency % Change

\%\Delta = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage move in an exchange rate between two points in time.

Cross Rate

Rate_{A/C} = Rate_{A/B} \times Rate_{B/C}

Derive the exchange rate between two currencies via a common third currency.

Bid-Ask Spread

Spread = Ask - Bid

The gap between the price to buy and to sell a currency — the dealer’s markup.

Spread Percentage

Spread\% = \dfrac{Ask - Bid}{Ask}\times 100\%

The bid-ask spread expressed as a percentage of the ask price.

Pip Value

Pip\ Value = \dfrac{Pip\ Size}{Rate}\times Lot

The monetary value of a one-pip move for a given trade size.

Appreciation / Depreciation

App\% = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage by which a currency strengthens (positive) or weakens (negative).

Purchasing Power Parity

S = \dfrac{P_{domestic}}{P_{foreign}}

The exchange rate that would equalize the price of an identical basket of goods across countries.

Real Exchange Rate

RER = S \times \dfrac{P_{foreign}}{P_{domestic}}

The nominal rate adjusted for price levels, measuring relative purchasing power.

Forward Exchange Rate

F = S \times \dfrac{1 + i_d}{1 + i_f}

The agreed future exchange rate implied by interest-rate differentials (covered interest parity).

Triangular Arbitrage

Profit = \left(\dfrac{1}{R_{AB}} \times R_{AC} \times R_{CB}\right) - 1

A riskless profit captured when three currencies’ cross rates are momentarily inconsistent.