Historical Exchange Rate Calculator
Fetching exchange rates…
Measuring the Distance Between Two Rates
Exchange rates are only interesting in comparison. A rate of 1.10 on its own says nothing; a rate of 1.10 against 1.20 a year earlier says a great deal. This calculator takes an amount and two rates — the one that applied then, the one that applies now — and reports both what the amount converts to under each and the percentage the rate itself moved. It is the difference, not either rate alone, that answers the question people are usually asking.
The Formula
Converted at New Rate = Amount × New Rate
% Change = ((New Rate − Old Rate) ÷ Old Rate) × 100
Conversions are rounded to six decimals and shown to two; the percentage change is rounded to four. Both rates must be positive and the amount cannot be negative. Note that the percentage change is calculated on the rates, not the converted amounts — though since the amount is a common factor, the two percentages are identical.
Rate Movement and What It Does to a Fixed Amount
| Old rate | New rate | At old rate | At new rate | % change |
|---|---|---|---|---|
| 1.20 | 1.10 | 1,200.00 | 1,100.00 | −8.33% |
| 1.20 | 1.32 | 1,200.00 | 1,320.00 | +10.00% |
| 1.00 | 1.05 | 1,000.00 | 1,050.00 | +5.00% |
Illustrative rate pairs, not observed historical quotes. The first row repays a second look: falling from 1.20 to 1.10 is a 8.33% move, but climbing back from 1.10 to 1.20 is a 9.09% move — the same journey in reverse, a different percentage, because the base has changed.
The Base Rate Determines the Percentage
An identical absolute movement produces a different percentage depending on where it started. A rate moving from 1.00 to 1.05 is a 5% change. The same 0.05 step from 1.20 to 1.25 is only about 4.17%. This is why quoting currency moves in "points" or raw decimals is nearly meaningless without the starting level attached, and why this calculator reports the percentage rather than the raw difference.
Questions This Answers
- "Would I have done better paying last year?" — comparing a recurring foreign payment against the rate that applied when the contract was signed.
- Gain and loss on foreign holdings — isolating how much of a change in value came from the currency rather than the asset.
- Budget variance — a project budgeted at one rate and settled at another, with the currency portion of the overrun quantified.
- Reporting — explaining a movement in translated figures between two reporting periods.
- Timing a transfer — measuring how far the rate has already moved before deciding whether to wait.
How to Use This Calculator
- Enter the Original Amount in the currency you hold.
- Enter the Old Exchange Rate — the rate that applied at the earlier date.
- Enter the New Exchange Rate — the rate at the later date or now.
- Submit to see both converted amounts side by side and the percentage the rate moved between them.
Related Calculations
- Purchasing Power Parity Calculator — compare a market rate against the rate implied by relative prices.
- Exchange Rate Calculator — convert an amount at a single rate.