Trend Strength Index Formula & How to Use It

The Trend Strength Index (TSI) calculator works out the strength of a price trend using two smoothed moving averages of price momentum. You enter a series of closing prices (or a single price and a reference period), and it returns a value between -100 and +100, where higher positive values indicate a stronger uptrend and lower negative values indicate a stronger downtrend.

Note: The calculator above uses a simplified two-point version to illustrate the formula. For a full TSI calculation you need a price series, not just two prices.

Formula

The Trend Strength Index (TSI) was introduced by William Blau in 1991. It measures the strength of a trend by comparing the smoothed momentum of price changes to the smoothed absolute momentum. The formula is:

TSI = 100 × (EMA(EMA(Momentum, n), m)) / (EMA(EMA(|Momentum|, n), m))

Where:

• Momentum = Current Price − Price n periods ago (typically n = 25)
• EMA = Exponential Moving Average
• n = Long smoothing period (typically 25)
• m = Short smoothing period (typically 13)
• |Momentum| = Absolute value of momentum (always positive)

The numerator is the double-smoothed momentum (the “signal” line), and the denominator is the double-smoothed absolute momentum (a measure of total price activity). Dividing one by the other normalises the result, so the TSI always falls between -100 and +100.

Worked Example

Using the default values from the calculator above (current price = 100, reference price = 90, short smoothing = 25, long smoothing = 13):

1. Calculate momentum: 100 − 90 = 10
2. Calculate absolute momentum: |10| = 10
3. Since we only have one momentum value, the EMA of a single number is that number itself. So EMA(EMA(10, 13), 25) = 10, and EMA(EMA(10, 13), 25) = 10.
4. TSI = 100 × (10 / 10) = 100

The calculator returns 100.00, which makes sense: with only one data point, the ratio of momentum to absolute momentum is 1, so the TSI is at its maximum. In practice, you need a full price series (at least 50–100 periods) for the TSI to be meaningful.

How the Double Smoothing Works

The key to the TSI is its double smoothing. First, a single EMA of momentum gives you a smoothed momentum line. Then a second EMA of that line smooths it further. This double smoothing removes short-term noise and makes the indicator less whippy than a simple momentum oscillator like the RSI.

The denominator uses the absolute value of momentum, which means it always grows as price movement increases, regardless of direction. This creates a ratio that tells you how much of the recent price activity is directional (trending) versus how much is just churning (noise). A TSI of +50 means that half of the recent price movement is upward directional; a TSI of -50 means half is downward directional.

Choosing the Smoothing Periods

The standard settings are 25 for the long smoothing and 13 for the short smoothing, based on Blau’s original work. However, traders often adjust these:

• Faster (more sensitive): Use shorter periods like 12 and 6. This gives more signals but more false positives.
• Slower (less sensitive): Use longer periods like 50 and 25. This filters out more noise but lags price action more.
• Intraday vs. daily: Shorter periods work better on intraday charts; longer periods suit daily or weekly charts.

There is no “best” setting. The right choice depends on the asset you are trading and your time horizon. Backtesting different settings on historical data is the only reliable way to find what works for a specific market.

How to Read the TSI Value

The TSI is an oscillator, so the value itself matters less than its position and direction. Common interpretations include:

• Above 0: Bullish momentum (prices are trending up on balance).
• Below 0: Bearish momentum (prices are trending down on balance).
• Above +25: Strong uptrend; some traders consider this overbought.
• Below -25: Strong downtrend; some traders consider this oversold.
• Crossing the zero line: A potential trend reversal signal. When TSI crosses from negative to positive, it suggests a new uptrend; crossing from positive to negative suggests a downtrend.
• Divergence: If price makes a new high but TSI makes a lower high, it may signal weakening momentum (bearish divergence). The opposite (bullish divergence) occurs when price makes a lower low but TSI makes a higher low.

Like all momentum indicators, the TSI works best in trending markets. In sideways or choppy markets, it will produce many false signals.

Common Mistakes and Limitations

The most common mistake is using the TSI on too few data points. The double EMA requires at least 2–3 times the long smoothing period of data to stabilise. With the standard 25/13 settings, you need at least 50–75 price bars before the indicator is reliable. Early values are heavily influenced by the starting point of the EMA calculation.

Another mistake is ignoring the scale. The TSI is not a percentage of price change; it is a ratio of smoothed momentum to smoothed absolute momentum. A TSI of 30 does not mean prices rose 30%. It means 30% of recent price activity was directional upward. Comparing TSI values across different assets is not meaningful because the smoothing adapts to each asset’s volatility.

The TSI also lags price. Because it uses double smoothing, it reacts more slowly than a single EMA or the RSI. This means it confirms trends but does not predict them. It is best used in conjunction with price action and other indicators, not as a standalone signal generator.

TSI vs. RSI and Other Oscillators

The TSI is often compared to the Relative Strength Index (RSI). Both are bounded oscillators, but they measure different things:

• RSI compares average gains to average losses over a fixed period (typically 14). It is a momentum oscillator that measures the speed and change of price movements.
• TSI compares double-smoothed momentum to double-smoothed absolute momentum. It is smoother and less prone to whipsaws.
• MACD is another momentum indicator, but it is unbounded and uses a different calculation (difference between two EMAs).

In practice, the TSI tends to give fewer but more reliable signals than the RSI, especially in strong trends. The RSI will hit overbought/oversold extremes quickly and stay there; the TSI is slower to reach extremes but also slower to reverse. Many traders use both: RSI for short-term timing, TSI for trend confirmation.

Frequently Asked Questions

What is the difference between TSI and the True Strength Index?

They are the same indicator. “True Strength Index” is the full name, and “Trend Strength Index” is a common alternative name. Both refer to William Blau’s 1991 formula using double-smoothed momentum.

Can the TSI go above 100 or below -100?

No. Because the numerator (smoothed momentum) can never exceed the denominator (smoothed absolute momentum), the ratio is always between -1 and +1, so the TSI is always between -100 and +100. In practice, values above +50 or below -50 are rare and indicate extremely strong trends.

What is the best TSI setting for day trading?

Day traders typically use shorter periods to reduce lag. A common choice is 12 for the long smoothing and 6 for the short smoothing. However, shorter settings produce more false signals, so many day traders combine the TSI with volume or price action filters. There is no universally “best” setting; it depends on the instrument and market conditions.

Does the TSI work on all timeframes?

Yes, the TSI can be applied to any timeframe, from 1-minute charts to monthly charts. The formula is scale-invariant. However, the optimal smoothing periods may differ. Higher timeframes (daily, weekly) generally work well with the standard 25/13 settings, while lower timeframes (1-minute, 5-minute) often benefit from shorter periods.

Is the TSI a leading or lagging indicator?

It is a lagging indicator. Because it uses double exponential smoothing, it reacts to price changes after they occur. It confirms trends rather than predicting them. Its main value is in filtering out noise and identifying the strength of an existing trend, not in calling reversals in advance.

How do I calculate the TSI in a spreadsheet?

You need a column of prices. First calculate momentum as price minus price 25 periods ago. Then calculate the EMA of that momentum with a 13-period smoothing, and the EMA of that result with a 25-period smoothing. Do the same for the absolute momentum. Finally, divide the double-smoothed momentum by the double-smoothed absolute momentum and multiply by 100. Most spreadsheet software has an EMA function or you can build it manually with the recursive formula EMA = (Price × k) + (Previous EMA × (1 − k)), where k = 2 / (period + 1).

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in p | Current price | - | 100 | 0
in r | Reference price (n periods ago) | - | 90 | 0
in s | Short smoothing period | - | 25 | 1
in l | Long smoothing period | - | 13 | 1
out tsi | Trend Strength Index | - | 100 * (ema(ema(p - r, l), s) / (ema(ema(abs(p - r), l), s))) | 2
out mom | Raw momentum (p - r) | - | p - r | 2