Functions

Some functions have default arguments, e.g. year(v=vector(time()) instant-vector). This means that there is one argument v which is an instant vector, which if not provided it will default to the value of the expression vector(time()).

Notes about the experimental native histograms:

• Ingesting native histograms has to be enabled via a feature flag. As long as no native histograms have been ingested into the TSDB, all functions will behave as usual.
• Functions that do not explicitly mention native histograms in their documentation (see below) will ignore histogram samples.
• Functions that do already act on native histograms might still change their behavior in the future.
• If a function requires the same bucket layout between multiple native histograms it acts on, it will automatically convert them appropriately. (With the currently supported bucket schemas, that’s always possible.)

abs()

abs(v instant-vector) returns the input vector with all sample values converted to their absolute value.

absent()

absent(v instant-vector) returns an empty vector if the vector passed to it has any elements (floats or native histograms) and a 1-element vector with the value 1 if the vector passed to it has no elements.

This is useful for alerting on when no time series exist for a given metric name and label combination.

absent(nonexistent{job="myjob"})
# => {job="myjob"}
absent(nonexistent{job="myjob",instance=~".*"})
# => {job="myjob"}
absent(sum(nonexistent{job="myjob"}))
# => {}

In the first two examples, absent() tries to be smart about deriving labels of the 1-element output vector from the input vector.

absent_over_time()

absent_over_time(v range-vector) returns an empty vector if the range vector passed to it has any elements (floats or native histograms) and a 1-element vector with the value 1 if the range vector passed to it has no elements.

This is useful for alerting on when no time series exist for a given metric name and label combination for a certain amount of time.

absent_over_time(nonexistent{job="myjob"}[1h])
# => {job="myjob"}
absent_over_time(nonexistent{job="myjob",instance=~".*"}[1h])
# => {job="myjob"}
absent_over_time(sum(nonexistent{job="myjob"})[1h:])
# => {}

In the first two examples, absent_over_time() tries to be smart about deriving labels of the 1-element output vector from the input vector.

ceil()

ceil(v instant-vector) rounds the sample values of all elements in v up to the nearest integer.

changes()

For each input time series, changes(v range-vector) returns the number of times its value has changed within the provided time range as an instant vector.

clamp()

clamp(v instant-vector, min scalar, max scalar) clamps the sample values of all elements in v to have a lower limit of min and an upper limit of max.

Special cases: - Return an empty vector if min > max - Return NaN if min or max is NaN

clamp_max()

clamp_max(v instant-vector, max scalar) clamps the sample values of all elements in v to have an upper limit of max.

clamp_min()

clamp_min(v instant-vector, min scalar) clamps the sample values of all elements in v to have a lower limit of min.

day_of_month()

day_of_month(v=vector(time()) instant-vector) returns the day of the month for each of the given times in UTC. Returned values are from 1 to 31.

day_of_week()

day_of_week(v=vector(time()) instant-vector) returns the day of the week for each of the given times in UTC. Returned values are from 0 to 6, where 0 means Sunday etc.

day_of_year()

day_of_year(v=vector(time()) instant-vector) returns the day of the year for each of the given times in UTC. Returned values are from 1 to 365 for non-leap years, and 1 to 366 in leap years.

days_in_month()

days_in_month(v=vector(time()) instant-vector) returns number of days in the month for each of the given times in UTC. Returned values are from 28 to 31.

delta()

delta(v range-vector) calculates the difference between the first and last value of each time series element in a range vector v, returning an instant vector with the given deltas and equivalent labels. The delta is extrapolated to cover the full time range as specified in the range vector selector, so that it is possible to get a non-integer result even if the sample values are all integers.

The following example expression returns the difference in CPU temperature between now and 2 hours ago:

delta(cpu_temp_celsius{host="zeus"}[2h])

delta acts on native histograms by calculating a new histogram where each compononent (sum and count of observations, buckets) is the difference between the respective component in the first and last native histogram in v. However, each element in v that contains a mix of float and native histogram samples within the range, will be missing from the result vector.

delta should only be used with gauges and native histograms where the components behave like gauges (so-called gauge histograms).

deriv()

deriv(v range-vector) calculates the per-second derivative of the time series in a range vector v, using simple linear regression. The range vector must have at least two samples in order to perform the calculation. When +Inf or -Inf are found in the range vector, the slope and offset value calculated will be NaN.

deriv should only be used with gauges.

exp()

exp(v instant-vector) calculates the exponential function for all elements in v. Special cases are:

• Exp(+Inf) = +Inf
• Exp(NaN) = NaN

floor()

floor(v instant-vector) rounds the sample values of all elements in v down to the nearest integer.

histogram_count() and histogram_sum()

Both functions only act on native histograms, which are an experimental feature. The behavior of these functions may change in future versions of Prometheus, including their removal from PromQL.

histogram_count(v instant-vector) returns the count of observations stored in a native histogram. Samples that are not native histograms are ignored and do not show up in the returned vector.

Similarly, histogram_sum(v instant-vector) returns the sum of observations stored in a native histogram.

Use histogram_count in the following way to calculate a rate of observations (in this case corresponding to “requests per second”) from a native histogram:

histogram_count(rate(http_request_duration_seconds[10m]))

The additional use of histogram_sum enables the calculation of the average of observed values (in this case corresponding to “average request duration”):

  histogram_sum(rate(http_request_duration_seconds[10m]))
/
  histogram_count(rate(http_request_duration_seconds[10m]))

histogram_fraction()

This function only acts on native histograms, which are an experimental feature. The behavior of this function may change in future versions of Prometheus, including its removal from PromQL.

For a native histogram, histogram_fraction(lower scalar, upper scalar, v instant-vector) returns the estimated fraction of observations between the provided lower and upper values. Samples that are not native histograms are ignored and do not show up in the returned vector.

For example, the following expression calculates the fraction of HTTP requests over the last hour that took 200ms or less:

histogram_fraction(0, 0.2, rate(http_request_duration_seconds[1h]))

The error of the estimation depends on the resolution of the underlying native histogram and how closely the provided boundaries are aligned with the bucket boundaries in the histogram.

+Inf and -Inf are valid boundary values. For example, if the histogram in the expression above included negative observations (which shouldn’t be the case for request durations), the appropriate lower boundary to include all observations less than or equal 0.2 would be -Inf rather than 0.

Whether the provided boundaries are inclusive or exclusive is only relevant if the provided boundaries are precisely aligned with bucket boundaries in the underlying native histogram. In this case, the behavior depends on the schema definition of the histogram. The currently supported schemas all feature inclusive upper boundaries and exclusive lower boundaries for positive values (and vice versa for negative values). Without a precise alignment of boundaries, the function uses linear interpolation to estimate the fraction. With the resulting uncertainty, it becomes irrelevant if the boundaries are inclusive or exclusive.

histogram_quantile()

histogram_quantile(φ scalar, b instant-vector) calculates the φ-quantile (0 ≤ φ ≤ 1) from a conventional histogram or from a native histogram. (See histograms and summaries for a detailed explanation of φ-quantiles and the usage of the (conventional) histogram metric type in general.)

Note that native histograms are an experimental feature. The behavior of this function when dealing with native histograms may change in future versions of Prometheus.

The conventional float samples in b are considered the counts of observations in each bucket of one or more conventional histograms. Each float sample must have a label le where the label value denotes the inclusive upper bound of the bucket. (Float samples without such a label are silently ignored.) The other labels and the metric name are used to identify the buckets belonging to each conventional histogram. The histogram metric type automatically provides time series with the _bucket suffix and the appropriate labels.

The native histogram samples in b are treated each individually as a separate histogram to calculate the quantile from.

As long as no naming collisions arise, b may contain a mix of conventional and native histograms.

Use the rate() function to specify the time window for the quantile calculation.

Example: A histogram metric is called http_request_duration_seconds (and therefore the metric name for the buckets of a conventional histogram is http_request_duration_seconds_bucket). To calculate the 90th percentile of request durations over the last 10m, use the following expression in case http_request_duration_seconds is a conventional histogram:

histogram_quantile(0.9, rate(http_request_duration_seconds_bucket[10m]))

For a native histogram, use the following expression instead:

histogram_quantile(0.9, rate(http_request_duration_seconds[10m]))

The quantile is calculated for each label combination in http_request_duration_seconds. To aggregate, use the sum() aggregator around the rate() function. Since the le label is required by histogram_quantile() to deal with conventional histograms, it has to be included in the by clause. The following expression aggregates the 90th percentile by job for conventional histograms:

histogram_quantile(0.9, sum by (job, le) (rate(http_request_duration_seconds_bucket[10m])))

When aggregating native histograms, the expression simplifies to:

histogram_quantile(0.9, sum by (job) (rate(http_request_duration_seconds[10m])))

To aggregate all conventional histograms, specify only the le label:

histogram_quantile(0.9, sum by (le) (rate(http_request_duration_seconds_bucket[10m])))

With native histograms, aggregating everything works as usual without any by clause:

histogram_quantile(0.9, sum(rate(http_request_duration_seconds[10m])))

The histogram_quantile() function interpolates quantile values by assuming a linear distribution within a bucket.

If b has 0 observations, NaN is returned. For φ < 0, -Inf is returned. For φ > 1, +Inf is returned. For φ = NaN, NaN is returned.

The following is only relevant for conventional histograms: If b contains fewer than two buckets, NaN is returned. The highest bucket must have an upper bound of +Inf. (Otherwise, NaN is returned.) If a quantile is located in the highest bucket, the upper bound of the second highest bucket is returned. A lower limit of the lowest bucket is assumed to be 0 if the upper bound of that bucket is greater than 0. In that case, the usual linear interpolation is applied within that bucket. Otherwise, the upper bound of the lowest bucket is returned for quantiles located in the lowest bucket.

holt_winters()

holt_winters(v range-vector, sf scalar, tf scalar) produces a smoothed value for time series based on the range in v. The lower the smoothing factor sf, the more importance is given to old data. The higher the trend factor tf, the more trends in the data is considered. Both sf and tf must be between 0 and 1.

holt_winters should only be used with gauges.

hour()

hour(v=vector(time()) instant-vector) returns the hour of the day for each of the given times in UTC. Returned values are from 0 to 23.

idelta()

idelta(v range-vector) calculates the difference between the last two samples in the range vector v, returning an instant vector with the given deltas and equivalent labels.

idelta should only be used with gauges.

increase()

increase(v range-vector) calculates the increase in the time series in the range vector. Breaks in monotonicity (such as counter resets due to target restarts) are automatically adjusted for. The increase is extrapolated to cover the full time range as specified in the range vector selector, so that it is possible to get a non-integer result even if a counter increases only by integer increments.

The following example expression returns the number of HTTP requests as measured over the last 5 minutes, per time series in the range vector:

increase(http_requests_total{job="api-server"}[5m])

increase acts on native histograms by calculating a new histogram where each component (sum and count of observations, buckets) is the increase between the respective component in the first and last native histogram in v. However, each element in v that contains a mix of float and native histogram samples within the range, will be missing from the result vector.

increase should only be used with counters and native histograms where the components behave like counters. It is syntactic sugar for rate(v) multiplied by the number of seconds under the specified time range window, and should be used primarily for human readability. Use rate in recording rules so that increases are tracked consistently on a per-second basis.

irate()

irate(v range-vector) calculates the per-second instant rate of increase of the time series in the range vector. This is based on the last two data points. Breaks in monotonicity (such as counter resets due to target restarts) are automatically adjusted for.

The following example expression returns the per-second rate of HTTP requests looking up to 5 minutes back for the two most recent data points, per time series in the range vector:

irate(http_requests_total{job="api-server"}[5m])

irate should only be used when graphing volatile, fast-moving counters. Use rate for alerts and slow-moving counters, as brief changes in the rate can reset the FOR clause and graphs consisting entirely of rare spikes are hard to read.

Note that when combining irate() with an aggregation operator (e.g. sum()) or a function aggregating over time (any function ending in _over_time), always take a irate() first, then aggregate. Otherwise irate() cannot detect counter resets when your target restarts.

label_join()

For each timeseries in v, label_join(v instant-vector, dst_label string, separator string, src_label_1 string, src_label_2 string, ...) joins all the values of all the src_labels using separator and returns the timeseries with the label dst_label containing the joined value. There can be any number of src_labels in this function.

label_join acts on float and histogram samples in the same way.

This example will return a vector with each time series having a foo label with the value a,b,c added to it:

label_join(up{job="api-server",src1="a",src2="b",src3="c"}, "foo", ",", "src1", "src2", "src3")

label_replace()

For each timeseries in v, label_replace(v instant-vector, dst_label string, replacement string, src_label string, regex string) matches the regular expression regex against the value of the label src_label. If it matches, the value of the label dst_label in the returned timeseries will be the expansion of replacement, together with the original labels in the input. Capturing groups in the regular expression can be referenced with $1, $2, etc. If the regular expression doesn’t match then the timeseries is returned unchanged.

label_replace acts on float and histogram samples in the same way.

This example will return timeseries with the values a:c at label service and a at label foo:

label_replace(up{job="api-server",service="a:c"}, "foo", "$1", "service", "(.*):.*")

ln()

ln(v instant-vector) calculates the natural logarithm for all elements in v. Special cases are:

• ln(+Inf) = +Inf
• ln(0) = -Inf
• ln(x < 0) = NaN
• ln(NaN) = NaN

log2()

log2(v instant-vector) calculates the binary logarithm for all elements in v. The special cases are equivalent to those in ln.

log10()

log10(v instant-vector) calculates the decimal logarithm for all elements in v. The special cases are equivalent to those in ln.

minute()

minute(v=vector(time()) instant-vector) returns the minute of the hour for each of the given times in UTC. Returned values are from 0 to 59.

month()

month(v=vector(time()) instant-vector) returns the month of the year for each of the given times in UTC. Returned values are from 1 to 12, where 1 means January etc.

predict_linear()

predict_linear(v range-vector, t scalar) predicts the value of time series t seconds from now, based on the range vector v, using simple linear regression. The range vector must have at least two samples in order to perform the calculation. When +Inf or -Inf are found in the range vector, the slope and offset value calculated will be NaN.

predict_linear should only be used with gauges.

rate()

rate(v range-vector) calculates the per-second average rate of increase of the time series in the range vector. Breaks in monotonicity (such as counter resets due to target restarts) are automatically adjusted for. Also, the calculation extrapolates to the ends of the time range, allowing for missed scrapes or imperfect alignment of scrape cycles with the range’s time period.

The following example expression returns the per-second rate of HTTP requests as measured over the last 5 minutes, per time series in the range vector:

rate(http_requests_total{job="api-server"}[5m])

rate acts on native histograms by calculating a new histogram where each compononent (sum and count of observations, buckets) is the rate of increase between the respective component in the first and last native histogram in v. However, each element in v that contains a mix of float and native histogram samples within the range, will be missing from the result vector.

rate should only be used with counters and native histograms where the components behave like counters. It is best suited for alerting, and for graphing of slow-moving counters.

Note that when combining rate() with an aggregation operator (e.g. sum()) or a function aggregating over time (any function ending in _over_time), always take a rate() first, then aggregate. Otherwise rate() cannot detect counter resets when your target restarts.

resets()

For each input time series, resets(v range-vector) returns the number of counter resets within the provided time range as an instant vector. Any decrease in the value between two consecutive float samples is interpreted as a counter reset. A reset in a native histogram is detected in a more complex way: Any decrease in any bucket, including the zero bucket, or in the count of observation constitutes a counter reset, but also the disappearance of any previously populated bucket, an increase in bucket resolution, or a decrease of the zero-bucket width.

resets should only be used with counters and counter-like native histograms.

If the range vector contains a mix of float and histogram samples for the same series, counter resets are detected separately and their numbers added up. The change from a float to a histogram sample is not considered a counter reset. Each float sample is compared to the next float sample, and each histogram is comprared to the next histogram.

round()

round(v instant-vector, to_nearest=1 scalar) rounds the sample values of all elements in v to the nearest integer. Ties are resolved by rounding up. The optional to_nearest argument allows specifying the nearest multiple to which the sample values should be rounded. This multiple may also be a fraction.

scalar()

Given a single-element input vector, scalar(v instant-vector) returns the sample value of that single element as a scalar. If the input vector does not have exactly one element, scalar will return NaN.

sgn()

sgn(v instant-vector) returns a vector with all sample values converted to their sign, defined as this: 1 if v is positive, -1 if v is negative and 0 if v is equal to zero.

sort()

sort(v instant-vector) returns vector elements sorted by their sample values, in ascending order. Native histograms are sorted by their sum of observations.

sort_desc()

Same as sort, but sorts in descending order.

sqrt()

sqrt(v instant-vector) calculates the square root of all elements in v.

time()

time() returns the number of seconds since January 1, 1970 UTC. Note that this does not actually return the current time, but the time at which the expression is to be evaluated.

timestamp()

timestamp(v instant-vector) returns the timestamp of each of the samples of the given vector as the number of seconds since January 1, 1970 UTC. It also works with histogram samples.

vector()

vector(s scalar) returns the scalar s as a vector with no labels.

year()

year(v=vector(time()) instant-vector) returns the year for each of the given times in UTC.

<aggregation>_over_time()

The following functions allow aggregating each series of a given range vector over time and return an instant vector with per-series aggregation results:

• avg_over_time(range-vector): the average value of all points in the specified interval.
• min_over_time(range-vector): the minimum value of all points in the specified interval.
• max_over_time(range-vector): the maximum value of all points in the specified interval.
• sum_over_time(range-vector): the sum of all values in the specified interval.
• count_over_time(range-vector): the count of all values in the specified interval.
• quantile_over_time(scalar, range-vector): the φ-quantile (0 ≤ φ ≤ 1) of the values in the specified interval.
• stddev_over_time(range-vector): the population standard deviation of the values in the specified interval.
• stdvar_over_time(range-vector): the population standard variance of the values in the specified interval.
• last_over_time(range-vector): the most recent point value in the specified interval.
• present_over_time(range-vector): the value 1 for any series in the specified interval.

Note that all values in the specified interval have the same weight in the aggregation even if the values are not equally spaced throughout the interval.

avg_over_time, sum_over_time, count_over_time, last_over_time, and present_over_time handle native histograms as expected. All other functions ignore histogram samples.

Trigonometric Functions

The trigonometric functions work in radians:

• acos(v instant-vector): calculates the arccosine of all elements in v (special cases).
• acosh(v instant-vector): calculates the inverse hyperbolic cosine of all elements in v (special cases).
• asin(v instant-vector): calculates the arcsine of all elements in v (special cases).
• asinh(v instant-vector): calculates the inverse hyperbolic sine of all elements in v (special cases).
• atan(v instant-vector): calculates the arctangent of all elements in v (special cases).
• atanh(v instant-vector): calculates the inverse hyperbolic tangent of all elements in v (special cases).
• cos(v instant-vector): calculates the cosine of all elements in v (special cases).
• cosh(v instant-vector): calculates the hyperbolic cosine of all elements in v (special cases).
• sin(v instant-vector): calculates the sine of all elements in v (special cases).
• sinh(v instant-vector): calculates the hyperbolic sine of all elements in v (special cases).
• tan(v instant-vector): calculates the tangent of all elements in v (special cases).
• tanh(v instant-vector): calculates the hyperbolic tangent of all elements in v (special cases).

The following are useful for converting between degrees and radians:

• deg(v instant-vector): converts radians to degrees for all elements in v.
• pi(): returns pi.
• rad(v instant-vector): converts degrees to radians for all elements in v.

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