Binary operators

Prometheus's query language supports basic logical and arithmetic operators. For operations between two instant vectors, the matching behavior can be modified.

Arithmetic binary operators

The following binary arithmetic operators exist in Prometheus:

  • + (addition)
  • - (subtraction)
  • * (multiplication)
  • / (division)
  • % (modulo)
  • ^ (power/exponentiation)

Binary arithmetic operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs.

Between two scalars, the behavior is obvious: they evaluate to another scalar that is the result of the operator applied to both scalar operands.

Between an instant vector and a scalar, the operator is applied to the value of every data sample in the vector. E.g. if a time series instant vector is multiplied by 2, the result is another vector in which every sample value of the original vector is multiplied by 2.

Between two instant vectors, a binary arithmetic operator is applied to each entry in the left-hand-side vector and its matching element in the right hand vector. The result is propagated into the result vector and the metric name is dropped. Entries for which no matching entry in the right-hand vector can be found are not part of the result.

Comparison binary operators

The following binary comparison operators exist in Prometheus:

  • == (equal)
  • != (not-equal)
  • > (greater-than)
  • < (less-than)
  • >= (greater-or-equal)
  • <= (less-or-equal)

Comparison operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs. By default they filter. Their behaviour can be modified by providing bool after the operator, which will return 0 or 1 for the value rather than filtering.

Between two scalars, the bool modifier must be provided and these operators result in another scalar that is either 0 (false) or 1 (true), depending on the comparison result.

Between an instant vector and a scalar, these operators are applied to the value of every data sample in the vector, and vector elements between which the comparison result is false get dropped from the result vector. If the bool modifier is provided, vector elements that would be dropped instead have the value 0 and vector elements that would be kept have the value 1.

Between two instant vectors, these operators behave as a filter by default, applied to matching entries. Vector elements for which the expression is not true or which do not find a match on the other side of the expression get dropped from the result, while the others are propagated into a result vector with their original (left-hand-side) metric names and label values. If the bool modifier is provided, vector elements that would have been dropped instead have the value 0 and vector elements that would be kept have the value 1 with the left-hand-side metric names and label values.

Logical/set binary operators

These logical/set binary operators are only defined between instant vectors:

  • and (intersection)
  • or (union)
  • unless (complement)

vector1 and vector2 results in a vector consisting of the elements of vector1 for which there are elements in vector2 with exactly matching label sets. Other elements are dropped. The metric name and values are carried over from the left-hand-side vector.

vector1 or vector2 results in a vector that contains all original elements (label sets + values) of vector1 and additionally all elements of vector2 which do not have matching label sets in vector1.

vector1 unless vector2 results in a vector consisting of the elements of vector1 for which there are no elements in vector2 with exactly matching label sets. All matching elements in both vectors are dropped.

Vector matching

Operations between vectors attempt to find a matching element in the right-hand-side vector for each entry in the left-hand side. There are two basic types of matching behavior:

One-to-one finds a unique pair of entries from each side of the operation. In the default case, that is an operation following the format vector1 <operator> vector2. Two entries match if they have the exact same set of labels and corresponding values. The ignoring keyword allows ignoring certain labels when matching, while the on keyword allows reducing the set of considered labels to a provided list:

<vector expr> <bin-op> ignoring(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) <vector expr>

Example input:

method_code:http_errors:rate5m{method="get", code="500"}  24
method_code:http_errors:rate5m{method="get", code="404"}  30
method_code:http_errors:rate5m{method="put", code="501"}  3
method_code:http_errors:rate5m{method="post", code="500"} 6
method_code:http_errors:rate5m{method="post", code="404"} 21

method:http_requests:rate5m{method="get"}  600
method:http_requests:rate5m{method="del"}  34
method:http_requests:rate5m{method="post"} 120

Example query:

method_code:http_errors:rate5m{code="500"} / ignoring(code) method:http_requests:rate5m

This returns a result vector containing the fraction of HTTP requests with status code of 500 for each method, as measured over the last 5 minutes. Without ignoring(code) there would have been no match as the metrics do not share the same set of labels. The entries with methods put and del have no match and will not show up in the result:

{method="get"}  0.04            //  24 / 600
{method="post"} 0.05            //   6 / 120

Many-to-one and one-to-many matchings refer to the case where each vector element on the "one"-side can match with multiple elements on the "many"-side. This has to be explicitly requested using the group_left or group_right modifier, where left/right determines which vector has the higher cardinality.

<vector expr> <bin-op> ignoring(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> ignoring(<label list>) group_right(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_right(<label list>) <vector expr>

The label list provided with the group modifier contains additional labels from the "one"-side to be included in the result metrics. For on a label can only appear in one of the lists. Every time series of the result vector must be uniquely identifiable.

Grouping modifiers can only be used for comparison and arithmetic. Operations as and, unless and or operations match with all possible entries in the right vector by default.

Example query:

method_code:http_errors:rate5m / ignoring(code) group_left method:http_requests:rate5m

In this case the left vector contains more than one entry per method label value. Thus, we indicate this using group_left. The elements from the right side are now matched with multiple elements with the same method label on the left:

{method="get", code="500"}  0.04            //  24 / 600
{method="get", code="404"}  0.05            //  30 / 600
{method="post", code="500"} 0.05            //   6 / 120
{method="post", code="404"} 0.175           //  21 / 120

Many-to-one and one-to-many matching are advanced use cases that should be carefully considered. Often a proper use of ignoring(<labels>) provides the desired outcome.

Aggregation operators

Prometheus supports the following built-in aggregation operators that can be used to aggregate the elements of a single instant vector, resulting in a new vector of fewer elements with aggregated values:

  • sum (calculate sum over dimensions)
  • min (select minimum over dimensions)
  • max (select maximum over dimensions)
  • avg (calculate the average over dimensions)
  • stddev (calculate population standard deviation over dimensions)
  • stdvar (calculate population standard variance over dimensions)
  • count (count number of elements in the vector)
  • count_values (count number of elements with the same value)
  • bottomk (smallest k elements by sample value)
  • topk (largest k elements by sample value)
  • quantile (calculate φ-quantile (0 ≤ φ ≤ 1) over dimensions)

These operators can either be used to aggregate over all label dimensions or preserve distinct dimensions by including a without or by clause.

<aggr-op>([parameter,] <vector expression>) [without|by (<label list>)] [keep_common]

parameter is only required for count_values, quantile, topk and bottomk. without removes the listed labels from the result vector, while all other labels are preserved the output. by does the opposite and drops labels that are not listed in the by clause, even if their label values are identical between all elements of the vector. The keep_common clause allows keeping those extra labels (labels that are identical between elements, but not in the by clause).

count_values outputs one time series per unique sample value. Each series has an additional label. The name of that label is given by the aggregation parameter, and the label value is the unique sample value. The value of each time series is the number of times that sample value was present.

topk and bottomk are different from other aggregators in that a subset of the input samples, including the original labels, are returned in the result vector. by and without are only used to bucket the input vector.


If the metric http_requests_total had time series that fan out by application, instance, and group labels, we could calculate the total number of seen HTTP requests per application and group over all instances via:

sum(http_requests_total) without (instance)

If we are just interested in the total of HTTP requests we have seen in all applications, we could simply write:


To count the number of binaries running each build version we could write:

count_values("version", build_version)

To get the 5 largest HTTP requests counts across all instances we could write:

topk(5, http_requests_total)

Binary operator precedence

The following list shows the precedence of binary operators in Prometheus, from highest to lowest.

  1. ^
  2. *, /, %
  3. +, -
  4. ==, !=, <=, <, >=, >
  5. and, unless
  6. or

Operators on the same precedence level are left-associative. For example, 2 * 3 % 2 is equivalent to (2 * 3) % 2. However ^ is right associative, so 2 * 3 ^ 2 is equivalent to 2 * (3 ^ 2).