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Fibonacci Levels

The retracement and extension prices of one swing, with where each ratio comes from.

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A swing, a ratio and a line:a place to look, and not a sign.

One swing

Result

Swing high

The highest price of the move.

Swing low

The lowest price of the move.

Direction of the move

Back to inputs

Size of the move

0.1000

1.1000 − 1.0000

61.8% retracement

1.0382

measured down from the high

A drawing of your own figures: the swing at the left and each level as a line across it, to scale. Retracements are full lines inside the move; extensions are dashed, beyond its end. Point at a line to read its price.

The move ran up from 1.0000 to 1.1000. Its retracement levels lie between 1.0764 (23.6%) and 1.0214 (78.6%), with 50% at 1.0500 and 61.8% at 1.0382; its extension levels lie above the high, from 1.1272 to 1.2618.

Retracement levels

Fractions of the move, measured back from where it ended. Under each ratio is where the number comes from.

Retracement levels of the swing: each ratio, where it comes from, and its price
Ratio	Price
23.6%A Fibonacci number divided by the one three places after it (21 ÷ 89): 0.618 cubed.	1.0764
38.2%A Fibonacci number divided by the one two places after it (21 ÷ 55): 0.618 squared.	1.0618
50%Not a Fibonacci ratio. Half the move, drawn by convention.	1.0500
61.8%A Fibonacci number divided by the next (34 ÷ 55): the ratio that neighbouring numbers settle towards.	1.0382
78.6%The square root of 0.618.	1.0214

Extension levels

Multiples of the move, measured from where it began, so each lies beyond where it ended.

Extension levels of the swing: each ratio, where it comes from, and its price
Ratio	Price
127.2%The square root of 1.618.	1.1272
161.8%A Fibonacci number divided by the one before it (55 ÷ 34): the golden ratio.	1.1618
261.8%1.618 squared: a Fibonacci number divided by the one two places before it (55 ÷ 21).	1.2618

SimulationA calculation on the figures you entered. Whether the levels have predictive value is a separate question: the evidence for it is weak and disputed, and part of what is seen near a level may simply be that many traders are watching the same lines. The levels are reference points, not forecasts. Educational information, not investment advice or a recommendation to trade.

How it works

Formula

after a rise: retracement = high − (high − low) × ratio; extension = low + (high − low) × ratio. After a fall the two are mirrored.

With your numbers

1Size of the move (high − low)1.1000 − 1.0000 = 0.1000
223.6% retracement: back down from the high1.1000 − 0.1000 × 0.236 = 1.0764
338.2% retracement: back down from the high1.1000 − 0.1000 × 0.382 = 1.0618
450% retracement: back down from the high1.1000 − 0.1000 × 0.5 = 1.0500
561.8% retracement: back down from the high1.1000 − 0.1000 × 0.618 = 1.0382
678.6% retracement: back down from the high1.1000 − 0.1000 × 0.786 = 1.0214
7127.2% extension: up from the low, past the high1.0000 + 0.1000 × 1.272 = 1.1272
8161.8% extension: up from the low, past the high1.0000 + 0.1000 × 1.618 = 1.1618
9261.8% extension: up from the low, past the high1.0000 + 0.1000 × 2.618 = 1.2618

Assumptions

Whether the levels have predictive value is a separate question: the evidence for it is weak and disputed, and part of what is seen near a level may simply be that many traders are watching the same lines. The levels are reference points, not forecasts.
The levels depend entirely on which high and which low you choose. Two people looking at the same chart often pick different swings and so draw different lines.
A retracement is measured back from the end of the move. An extension here is measured from the start of the move and lies beyond its end; the three-point extension tool on a trading platform projects from a later point instead and gives different prices.
50% is not a Fibonacci ratio. It is included because chart users draw it by convention.
The starting figures are an example, not a market’s price. Replace them with the swing you are looking at.

Terms used

In plain language

Fractions of a move that has already happened.

Take one swing, from a low to a high or from a high to a low. A retracement level is the price at which a given fraction of that move would have been given back. An extension level is the price at which the move would have grown to a given multiple of itself. That is the whole calculation: one subtraction and one multiplication for each line.

The ratios come from the Fibonacci sequence, in which each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Divide any number by the next and the answer settles towards 0.618: that is the 61.8% level, the ratio of neighbouring Fibonacci numbers. Skip one place and it is 0.382; skip two and it is 0.236. Divide the other way and it is 1.618. The 78.6% and 127.2% levels are the square roots of 0.618 and 1.618. The 50% level is not a Fibonacci ratio at all, and is included by convention.

The golden ratio gives these tools their arithmetic. Whether the levels have predictive value is a separate question: the evidence for it is weak and disputed, and part of what is seen near a level may simply be that many traders are watching the same lines. The levels are reference points, not forecasts.

The lines also depend on a choice the formula cannot make: which high and which low. Different swings give different levels, and with enough lines on a chart a price will always be near one of them.

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Ratio

Price

23.6%A Fibonacci number divided by the one three places after it (21 ÷ 89): 0.618 cubed.

1.0764

38.2%A Fibonacci number divided by the one two places after it (21 ÷ 55): 0.618 squared.

1.0618

50%Not a Fibonacci ratio. Half the move, drawn by convention.

1.0500

61.8%A Fibonacci number divided by the next (34 ÷ 55): the ratio that neighbouring numbers settle towards.

1.0382

78.6%The square root of 0.618.

1.0214

Ratio

Price

127.2%The square root of 1.618.

1.1272

161.8%A Fibonacci number divided by the one before it (55 ÷ 34): the golden ratio.

1.1618

261.8%1.618 squared: a Fibonacci number divided by the one two places before it (55 ÷ 21).

1.2618

How it works

Formula

after a rise: retracement = high − (high − low) × ratio; extension = low + (high − low) × ratio. After a fall the two are mirrored.

With your numbers

1Size of the move (high − low)1.1000 − 1.0000 = 0.1000

223.6% retracement: back down from the high1.1000 − 0.1000 × 0.236 = 1.0764

338.2% retracement: back down from the high1.1000 − 0.1000 × 0.382 = 1.0618

450% retracement: back down from the high1.1000 − 0.1000 × 0.5 = 1.0500

561.8% retracement: back down from the high1.1000 − 0.1000 × 0.618 = 1.0382

678.6% retracement: back down from the high1.1000 − 0.1000 × 0.786 = 1.0214

7127.2% extension: up from the low, past the high1.0000 + 0.1000 × 1.272 = 1.1272

8161.8% extension: up from the low, past the high1.0000 + 0.1000 × 1.618 = 1.1618

9261.8% extension: up from the low, past the high1.0000 + 0.1000 × 2.618 = 1.2618

Assumptions

Whether the levels have predictive value is a separate question: the evidence for it is weak and disputed, and part of what is seen near a level may simply be that many traders are watching the same lines. The levels are reference points, not forecasts.

The levels depend entirely on which high and which low you choose. Two people looking at the same chart often pick different swings and so draw different lines.

A retracement is measured back from the end of the move. An extension here is measured from the start of the move and lies beyond its end; the three-point extension tool on a trading platform projects from a later point instead and gives different prices.

50% is not a Fibonacci ratio. It is included because chart users draw it by convention.

The starting figures are an example, not a market’s price. Replace them with the swing you are looking at.

Terms used