Fibonacci calculator

How do you calculate Fibonacci retracement levels?

Measure the range of the move, swing high - swing low, then step back from the end of the move by each ratio. In an uptrend the move ends at the high, so retracement level = high - range x ratio. In a downtrend it ends at the low, so the level is low + range x ratio.

The default inputs describe a rise from 100 to 150, a range of 50. The levels are:

The 0% level is the high itself and 100% is the low. The calculator's headline is the 61.8% level, because it is the one most often searched for, and the table under the result lists every level with its distance from the end of the swing.

Where do the Fibonacci ratios come from?

The Fibonacci sequence starts 1, 1 and adds the last two numbers to get the next: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. Divide a number by the one after it and the answer settles toward 0.618: 3 / 5 is 0.6, 8 / 13 is 0.6154, 21 / 34 is 0.6176 and 89 / 144 is 0.6181. Divide by the number after that and it settles toward 0.382 (55 / 144 is 0.3819), and three places along toward 0.236 (34 / 144 is 0.2361). Divide the other way and you approach 1.618 and 2.618 (144 / 89 and 233 / 89 are both 1.6180 and 2.6180 to four places).

The limits are powers of the golden ratio, phi = 1.6180340: 0.618 is 1 / phi, 0.382 is 1 / phi squared, 0.236 is 1 / phi cubed and 2.618 is phi squared. Two common levels come from roots instead: 78.6% is the square root of 0.618, which is 0.7861, and 127.2% is the square root of 1.618, which is 1.2720. The 138.2% level is 1 + 0.382.

The 50% level is not a Fibonacci ratio at all. It is simply half the move, and charting tools include it alongside the others by convention.

Fibonacci extension levels: two ways to measure them

Extensions sit beyond the end of the swing, in the direction of the move. The ratios are standard, but where they are measured from is not, and both conventions are in common use:

• From the start of the swing (the default): level = start + range x ratio, so 100% is the swing end and 161.8% lies 0.618 of the range beyond it.
• From the end of the swing: level = end + range x ratio, so the 161.8% level lies a full 1.618 ranges past the end.

The same label can mean a price 50 points apart, so before comparing a level with a chart, an article or another calculator, check which way it was measured. Switch the convention under How extensions are measured and both the table and the ladder follow.

Fibonacci retracement in a downtrend

In a fall the move ends at the low, so retracements are measured up from it: level = low + range x ratio. For a fall from 150 to 100, the 23.6% level is 111.80, 38.2% is 119.10, 50% is 125.00, 61.8% is 130.90 and 78.6% is 139.30.

Extensions then lie below the low. Measured from the start of the swing they are 86.40 at 127.2%, 69.10 at 161.8% and 19.10 at 261.8%. On a large fall the deeper extensions can work out below zero: for a drop from 100 to 50, the 261.8% level measured from the start would be -30.90, which no share price can reach, so the calculator shows it as below zero rather than as a price.

Choosing the direction matters. The same two prices give different levels in each, because the ratios are counted back from whichever end the move finished at.

Fibonacci calculator for forex: pips and decimals

Most currency pairs are quoted to five decimals and yen pairs to three, so pick the matching option under Decimal places. Rounding to two decimals on EUR/USD would hide the very differences the levels are meant to show.

Example. EUR/USD rises from 1.08000 to 1.10000, a range of 0.02000, or 200 pips. The 38.2% retracement is 1.09236, 76.4 pips below the high; the 50% level is 1.09000; the 61.8% retracement is 1.08764, 123.6 pips below the high; and the 161.8% extension from the start of the swing is 1.11236.

The prices are typed as your chart quotes them and are never converted, so the page has no currency selector. To put a money value on a distance in pips, use the pip value calculator.

Worked examples on shares in pounds and euros

• A UK share in pounds. The price rises from £4.20 to £5.00, a range of £0.80, or 19.05% of the low. The 38.2% retracement is £4.6944, the 50% level £4.60 and the 61.8% retracement £4.5056. Measured from the start, the 127.2% extension is £5.2176 and the 161.8% extension £5.4944.
• A share in euros, falling. The price drops from €86 to €74, a range of €12. Retracements are measured up from the low: €76.83 at 23.6%, €78.58 at 38.2%, €80.00 at 50%, €81.42 at 61.8% and €83.43 at 78.6%. Below the low, the 161.8% extension is €66.58.

The arithmetic does not care what currency the chart is in. A share quoted in pence works the same way: enter 420 and 500 and the levels come out in pence.

How to calculate Fibonacci levels in Excel or Google Sheets

Put the swing high in B1, the swing low in B2 and the ratios down column A from A4: 0.236, 0.382, 0.5, 0.618, 0.786. For an uptrend enter =$B$1-($B$1-$B$2)*A4 in B4 and fill down; for the default inputs B7 returns 119.1. For a downtrend use =$B$2+($B$1-$B$2)*A4.

For extensions measured from the start of an upward swing, put 1.272, 1.382, 1.618 and 2.618 in column A and use =$B$2+($B$1-$B$2)*A4, which gives 180.9 for 1.618. To measure from the end instead, use =$B$1+($B$1-$B$2)*A4.

What Fibonacci levels can and cannot tell you

The levels are fixed fractions of a distance you chose. The calculator places them exactly; it cannot say whether price will pause, reverse or pass straight through any of them, and nothing on this page suggests that it will. With five retracement levels between the high and the low, some level is usually close to wherever price happens to turn, which is worth keeping in mind when reading charts after the fact.

• Choosing the swing points. Two people can pick different highs and lows from the same chart and get different levels. Use the same rule every time, such as closing prices or the extreme wicks.
• Mixing up the direction. Retracements are counted back from where the move ended.
• Comparing extensions measured different ways. Check the convention first.
• Rounding too early. Use the decimals your instrument is quoted in.
• Using 76.4% and 78.6% interchangeably. Some tools show 76.4%, which is 1 - 0.236; on the default upswing it sits at 111.80, not 110.70.

Glossary

Swing high and swing low: the highest and lowest prices of the move being measured. Range: swing high minus swing low. Retracement: a move back against the trend, measured as a share of the range. Extension: a level beyond the end of the swing, in the direction of the move. Golden ratio (phi): 1.6180340, the limit of the ratio between consecutive Fibonacci numbers. Pip: the standard price step in forex, 0.0001 on most pairs and 0.01 on yen pairs.

Frequently asked questions

Courses behind chart levels

Sources and review