diff()

diff(x, lag = 1, differences = 1)

The diff() function computes lagged differences between consecutive elements in a numeric vector. By default, it calculates the first-order difference (each element minus its predecessor), which is essential for analyzing changes over time, detecting trends, and computing rate of change.

Syntax

diff(x, lag = 1, differences = 1)

Parameters

Parameter	Type	Default	Description
x	numeric	—	A numeric vector or an object that can be coerced to numeric
lag	integer	1	The number of lags to use for computing differences
differences	integer	1	The number of times differences are recursively applied

Examples

Basic usage

# Simple first-order differences
x <- c(10, 15, 13, 18, 20)
diff(x)
# [1]  5 -2  5  2

# Each element minus its predecessor
# 15-10=5, 13-15=-2, 18-13=5, 20-18=2

Computing percentage changes

# Stock prices over 5 days
prices <- c(100, 105, 102, 110, 108)

# Daily price changes
daily_change <- diff(prices)
daily_change
# [1]  5 -3  8 -2

# Percentage change (need to divide by previous value)
pct_change <- daily_change / prices[-length(prices)] * 100
pct_change
# [1]  5.000000 -2.857143  7.843137 -1.818182

Using lag parameter

x <- c(1, 3, 6, 10, 15, 21)

# Default lag=1: consecutive differences
diff(x)
# [1] 2 3 4 5 6

# Lag=2: differences between elements 2 apart
diff(x, lag = 2)
# [1] 5 7 9 11
# 6-1=5, 10-3=7, 15-6=9, 21-10=11

Using differences parameter

x <- c(1, 3, 6, 10, 15, 21)

# First-order differences (default)
diff(x)
# [1] 2 3 4 5 6

# Second-order differences (difference of differences)
diff(x, differences = 2)
# [1] 1 1 1 1
# First: 2,3,4,5,6
# Then: 3-2=1, 4-3=1, 5-4=1, 6-5=1

Common Patterns

Detecting sign changes

# Find where the direction of change flips
changes <- diff(x)
signs <- sign(changes)
which(signs[-length(signs)] != signs[-1]) + 1

Computing running totals first

# First accumulate, then diff recovers original
x <- c(10, 25, 30, 55, 60)
cumsum(x)
# [1]  10  35  65 120 180

# diff(cumsum(x)) returns x[-length(x)]
diff(cumsum(x))
# [1] 10 25 30 55

Working with time series

# Simulated daily temperatures
temps <- c(20, 22, 25, 23, 19, 21, 24)

# Identify warming/cooling trends
diff(temps)
# [1]  2  3 -2 -4  2  3

# Positive = warming, Negative = cooling

See Also

• round()
• table()
• tapply()