diff --git a/app/vmselect/promql/eval.go b/app/vmselect/promql/eval.go
index 952e8d572..570257eb2 100644
--- a/app/vmselect/promql/eval.go
+++ b/app/vmselect/promql/eval.go
@@ -472,22 +472,6 @@ func removeNanValues(dstValues []float64, dstTimestamps []int64, values []float6
 	return dstValues, dstTimestamps
 }
 
-func getMaxPointsPerRollup() int {
-	maxPointsPerRollupOnce.Do(func() {
-		n := memory.Allowed() / 16 / 8
-		if n <= 16 {
-			n = 16
-		}
-		maxPointsPerRollup = n
-	})
-	return maxPointsPerRollup
-}
-
-var (
-	maxPointsPerRollup     int
-	maxPointsPerRollupOnce sync.Once
-)
-
 var (
 	rollupResultCacheFullHits    = metrics.NewCounter(`vm_rollup_result_cache_full_hits_total`)
 	rollupResultCachePartialHits = metrics.NewCounter(`vm_rollup_result_cache_partial_hits_total`)
@@ -533,12 +517,17 @@ func evalRollupFuncWithMetricExpr(ec *EvalConfig, name string, rf rollupFunc, me
 	// Verify timeseries fit available memory after the rollup.
 	// Take into account points from tssCached.
 	pointsPerTimeseries := 1 + (ec.End-ec.Start)/ec.Step
-	if uint64(pointsPerTimeseries) > uint64(getMaxPointsPerRollup()/rssLen/len(rcs)) {
+	rollupPoints := mulNoOverflow(pointsPerTimeseries, int64(rssLen*len(rcs)))
+	rollupMemorySize := mulNoOverflow(rollupPoints, 16)
+	rml := getRollupMemoryLimiter()
+	if !rml.Get(uint64(rollupMemorySize)) {
 		rss.Cancel()
-		return nil, fmt.Errorf("cannot process more than %d data points for %d time series with %d points in each time series; "+
-			"possible solutions are: reducing the number of matching time series; switching to node with more RAM; increasing `step` query arg (%gs)",
-			getMaxPointsPerRollup(), rssLen*len(rcs), pointsPerTimeseries, float64(ec.Step)/1e3)
+		return nil, fmt.Errorf("not enough memory for processing %d data points across %d time series with %d points in each time series; "+
+			"possible solutions are: reducing the number of matching time series; switching to node with more RAM; "+
+			"increasing -memory.allowedPercent; increasing `step` query arg (%gs)",
+			rollupPoints, rssLen*len(rcs), pointsPerTimeseries, float64(ec.Step)/1e3)
 	}
+	defer rml.Put(uint64(rollupMemorySize))
 
 	// Evaluate rollup
 	tss := make([]*timeseries, 0, rssLen*len(rcs))
@@ -575,6 +564,18 @@ func evalRollupFuncWithMetricExpr(ec *EvalConfig, name string, rf rollupFunc, me
 	return tss, nil
 }
 
+var (
+	rollupMemoryLimiter     memoryLimiter
+	rollupMemoryLimiterOnce sync.Once
+)
+
+func getRollupMemoryLimiter() *memoryLimiter {
+	rollupMemoryLimiterOnce.Do(func() {
+		rollupMemoryLimiter.MaxSize = uint64(memory.Allowed()) / 4
+	})
+	return &rollupMemoryLimiter
+}
+
 func getRollupConfigs(name string, rf rollupFunc, start, end, step, window int64, sharedTimestamps []int64) (func(values []float64, timestamps []int64), []*rollupConfig) {
 	preFunc := func(values []float64, timestamps []int64) {}
 	if rollupFuncsRemoveCounterResets[name] {
@@ -653,3 +654,11 @@ func evalTime(ec *EvalConfig) []*timeseries {
 	}
 	return rv
 }
+
+func mulNoOverflow(a, b int64) int64 {
+	if math.MaxInt64/b < a {
+		// Overflow
+		return math.MaxInt64
+	}
+	return a * b
+}
diff --git a/app/vmselect/promql/memory_limiter.go b/app/vmselect/promql/memory_limiter.go
new file mode 100644
index 000000000..e9a76b143
--- /dev/null
+++ b/app/vmselect/promql/memory_limiter.go
@@ -0,0 +1,33 @@
+package promql
+
+import (
+	"sync"
+
+	"github.com/VictoriaMetrics/VictoriaMetrics/lib/logger"
+)
+
+type memoryLimiter struct {
+	MaxSize uint64
+
+	mu    sync.Mutex
+	usage uint64
+}
+
+func (ml *memoryLimiter) Get(n uint64) bool {
+	ml.mu.Lock()
+	ok := n <= ml.MaxSize && ml.MaxSize-n >= ml.usage
+	if ok {
+		ml.usage += n
+	}
+	ml.mu.Unlock()
+	return ok
+}
+
+func (ml *memoryLimiter) Put(n uint64) {
+	ml.mu.Lock()
+	if n > ml.usage {
+		logger.Panicf("BUG: n=%d cannot exceed %d", n, ml.usage)
+	}
+	ml.usage -= n
+	ml.mu.Unlock()
+}
diff --git a/app/vmselect/promql/memory_limiter_test.go b/app/vmselect/promql/memory_limiter_test.go
new file mode 100644
index 000000000..4477678e4
--- /dev/null
+++ b/app/vmselect/promql/memory_limiter_test.go
@@ -0,0 +1,56 @@
+package promql
+
+import (
+	"testing"
+)
+
+func TestMemoryLimiter(t *testing.T) {
+	var ml memoryLimiter
+	ml.MaxSize = 100
+
+	// Allocate memory
+	if !ml.Get(10) {
+		t.Fatalf("cannot get 10 out of %d bytes", ml.MaxSize)
+	}
+	if ml.usage != 10 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 10)
+	}
+	if !ml.Get(20) {
+		t.Fatalf("cannot get 20 out of 90 bytes")
+	}
+	if ml.usage != 30 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 30)
+	}
+	if ml.Get(1000) {
+		t.Fatalf("unexpected get for 1000 bytes")
+	}
+	if ml.usage != 30 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 30)
+	}
+	if ml.Get(71) {
+		t.Fatalf("unexpected get for 71 bytes")
+	}
+	if ml.usage != 30 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 30)
+	}
+	if !ml.Get(70) {
+		t.Fatalf("cannot get 70 bytes")
+	}
+	if ml.usage != 100 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 100)
+	}
+
+	// Return memory back
+	ml.Put(10)
+	ml.Put(70)
+	if ml.usage != 20 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 20)
+	}
+	if !ml.Get(30) {
+		t.Fatalf("cannot get 30 bytes")
+	}
+	ml.Put(50)
+	if ml.usage != 0 {
+		t.Fatalf("unexpected usage; got %d; want %d", ml.usage, 0)
+	}
+}