diff --git a/src/dto.rs b/src/dto.rs
index 7a89a2b..05171af 100644
--- a/src/dto.rs
+++ b/src/dto.rs
@@ -47,6 +47,19 @@ pub struct StatsDto {
     pub last_sequence: Option<u64>,
     pub first_timestamp_ms: Option<i64>,
     pub last_timestamp_ms: Option<i64>,
+    /// Ticket 011: a running, *approximate* estimate of the in-memory heap
+    /// held by currently-ingested logs, in bytes. "Approximate" because it
+    /// only counts each `IngestedLine::text`'s UTF-8 byte length — it does
+    /// not account for `String`'s allocator overhead/capacity slack, the
+    /// `BTreeMap`/`IndexKey` node overhead the text is stored under, or any
+    /// derived data (bucket values, params) the line produces elsewhere in
+    /// the index. That's judged the best cheap proxy for "how much memory is
+    /// this log's text costing us": it's O(1) to compute per log (`text.len()`,
+    /// already an interned byte count for UTF-8 `String`), moves in lockstep
+    /// with the dominant cost (raw log text, which is usually much larger
+    /// than the fixed per-entry bookkeeping), and needs no per-entry
+    /// bookkeeping beyond what eviction already tracks.
+    pub approx_bytes_total: u64,
 }
 
 #[derive(Debug, Deserialize)]
diff --git a/src/engine.rs b/src/engine.rs
index 741cf0c..d9b11ee 100644
--- a/src/engine.rs
+++ b/src/engine.rs
@@ -128,18 +128,23 @@ pub async fn run(mut rx: mpsc::Receiver<EngineMessage>, settings: SettingsHandle
     let mut metric_sample_sequence: u64 = 0;
     // Per-rule rolling windows/seen-value sets, keyed by rule id; lives only as long as this loop (no restart persistence).
     let mut alert_states: HashMap<String, AlertRuntimeState> = HashMap::new();
+    // Ticket 011: running total of `approx_log_bytes` (see that function) across
+    // every currently-ingested log, kept in lockstep with `log_count` — incremented
+    // here on ingest, decremented in `evict_excess_logs` when a log is dropped.
+    let mut approx_bytes_total: u64 = 0;
 
     while let Some(message) = rx.recv().await {
         match message {
             EngineMessage::Ingest(line) => {
                 let IngestedLine { sequence, timestamp, text } = line;
+                approx_bytes_total += approx_log_bytes(&text);
                 index.insert(
                     IndexKey::IngestedLog { sequence, timestamp },
                     DataValue::LogLiteral { text: text.clone() },
                 );
                 log_count += 1;
                 apply_all_metrics(&mut index, sequence, timestamp, &text);
-                evict_excess_logs(&mut index, &mut log_count, max_logs);
+                evict_excess_logs(&mut index, &mut log_count, max_logs, &mut approx_bytes_total);
 
                 // Evaluate alert rules against just this line, then hand any fired rule off to delivery via tokio::spawn so it stays off the hot path.
                 let (rules, ntfy_topic, ntfy_server) = {
@@ -169,7 +174,7 @@ pub async fn run(mut rx: mpsc::Receiver<EngineMessage>, settings: SettingsHandle
             }
             EngineMessage::SetMaxLogs(new_max) => {
                 max_logs = new_max;
-                evict_excess_logs(&mut index, &mut log_count, max_logs);
+                evict_excess_logs(&mut index, &mut log_count, max_logs, &mut approx_bytes_total);
             }
             EngineMessage::DeclareParam { request, respond_to } => {
                 let result = declare_param(&mut index, request);
@@ -188,7 +193,7 @@ pub async fn run(mut rx: mpsc::Receiver<EngineMessage>, settings: SettingsHandle
                 let _ = respond_to.send(existed);
             }
             EngineMessage::Query { query, respond_to } => {
-                let response = handle_query(&index, query);
+                let response = handle_query(&index, query, approx_bytes_total);
                 let _ = respond_to.send(response);
             }
         }
@@ -723,11 +728,24 @@ fn derive_log_params(
     params
 }
 
-/// Bucket values already derived from an evicted log are left in place — buckets are aggregate data, not raw logs, so they're not retroactively pruned.
+/// Ticket 011's approximate per-log byte size: see `StatsDto::approx_bytes_total`'s
+/// doc comment for why the raw UTF-8 text length is the chosen proxy rather than a
+/// full struct-size estimate.
+fn approx_log_bytes(text: &str) -> u64 {
+    text.len() as u64
+}
+
+/// Evicts the oldest (lowest-`sequence`) ingested logs until `log_count` is
+/// back at or under `max_logs`. `sequence` numbering is not renumbered on
+/// eviction, and any `Bucket` values already derived from an evicted log are
+/// left in place — buckets are aggregate data, not raw logs, so they're not
+/// retroactively pruned. `approx_bytes_total` (ticket 011) is decremented by
+/// each evicted log's approximate size, mirroring the increment on ingest.
 fn evict_excess_logs(
     index: &mut BTreeMap<IndexKey, DataValue>,
     log_count: &mut usize,
     max_logs: Option<usize>,
+    approx_bytes_total: &mut u64,
 ) {
     let Some(max_logs) = max_logs else { return };
     while *log_count > max_logs {
@@ -738,6 +756,9 @@ fn evict_excess_logs(
         else {
             break;
         };
+        if let Some(DataValue::LogLiteral { text }) = index.get(&oldest_key) {
+            *approx_bytes_total = approx_bytes_total.saturating_sub(approx_log_bytes(text));
+        }
         index.remove(&oldest_key);
         *log_count -= 1;
     }
@@ -754,7 +775,11 @@ fn logs_range(index: &BTreeMap<IndexKey, DataValue>) -> impl Iterator<Item = (u6
     })
 }
 
-fn handle_query(index: &BTreeMap<IndexKey, DataValue>, query: EngineQuery) -> EngineResponse {
+fn handle_query(
+    index: &BTreeMap<IndexKey, DataValue>,
+    query: EngineQuery,
+    approx_bytes_total: u64,
+) -> EngineResponse {
     match query {
         EngineQuery::Logs(params) => {
             let compiled_filter = match params.filter.as_deref() {
@@ -836,6 +861,7 @@ fn handle_query(index: &BTreeMap<IndexKey, DataValue>, query: EngineQuery) -> En
                 last_sequence,
                 first_timestamp_ms,
                 last_timestamp_ms,
+                approx_bytes_total,
             })
         }
         EngineQuery::ParamDeclarations => {
@@ -1080,26 +1106,34 @@ mod tests {
     fn evict_excess_logs_drops_oldest_sequences_first() {
         let mut index = BTreeMap::new();
         let mut log_count = 0;
+        let mut approx_bytes_total = 0u64;
         for sequence in 0..5u64 {
+            let text = format!("line {sequence}");
+            approx_bytes_total += approx_log_bytes(&text);
             index.insert(
                 IndexKey::IngestedLog { sequence, timestamp: Timestamp::from_millis(sequence as i64) },
-                DataValue::LogLiteral { text: format!("line {sequence}") },
+                DataValue::LogLiteral { text },
             );
             log_count += 1;
         }
 
-        evict_excess_logs(&mut index, &mut log_count, Some(3));
+        evict_excess_logs(&mut index, &mut log_count, Some(3), &mut approx_bytes_total);
 
         assert_eq!(log_count, 3);
         let remaining: Vec<_> = logs_range(&index).map(|(seq, _, _)| seq).collect();
         assert_eq!(remaining, vec![2, 3, 4]);
+        let expected_bytes: u64 =
+            remaining.iter().map(|seq| approx_log_bytes(&format!("line {seq}"))).sum();
+        assert_eq!(approx_bytes_total, expected_bytes);
     }
 
     #[test]
     fn evict_excess_logs_is_noop_when_unlimited_or_under_cap() {
         let mut index = BTreeMap::new();
         let mut log_count = 0;
+        let mut approx_bytes_total = 0u64;
         for sequence in 0..3u64 {
+            approx_bytes_total += approx_log_bytes("x");
             index.insert(
                 IndexKey::IngestedLog { sequence, timestamp: Timestamp::from_millis(sequence as i64) },
                 DataValue::LogLiteral { text: "x".to_string() },
@@ -1107,11 +1141,13 @@ mod tests {
             log_count += 1;
         }
 
-        evict_excess_logs(&mut index, &mut log_count, None);
+        evict_excess_logs(&mut index, &mut log_count, None, &mut approx_bytes_total);
         assert_eq!(log_count, 3);
+        assert_eq!(approx_bytes_total, 3);
 
-        evict_excess_logs(&mut index, &mut log_count, Some(10));
+        evict_excess_logs(&mut index, &mut log_count, Some(10), &mut approx_bytes_total);
         assert_eq!(log_count, 3);
+        assert_eq!(approx_bytes_total, 3);
     }
 
     #[test]
@@ -1773,6 +1809,7 @@ mod tests {
                 start_ms: None,
                 end_ms: None,
             },
+            0,
         );
         match response {
             EngineResponse::Promql(Err(message)) => assert!(!message.is_empty()),
@@ -1793,6 +1830,7 @@ mod tests {
                 start_ms: None,
                 end_ms: None,
             },
+            0,
         );
         match response {
             EngineResponse::Promql(Ok(series)) => {
@@ -1832,7 +1870,7 @@ mod tests {
         ingest_log(&mut index, 2, "still fine");
         ingest_log(&mut index, 3, "another error here");
 
-        match handle_query(&index, logs_query(Some(r#"regex("error")"#))) {
+        match handle_query(&index, logs_query(Some(r#"regex("error")"#)), 0) {
             EngineResponse::Logs(entries) => {
                 let sequences: Vec<u64> = entries.iter().map(|e| e.sequence).collect();
                 assert_eq!(sequences, vec![1, 3]);
@@ -1848,7 +1886,7 @@ mod tests {
             ingest_log(&mut index, i, &format!("line {i}"));
         }
 
-        match handle_query(&index, logs_query(Some("sequence<2"))) {
+        match handle_query(&index, logs_query(Some("sequence<2")), 0) {
             EngineResponse::Logs(entries) => {
                 let sequences: Vec<u64> = entries.iter().map(|e| e.sequence).collect();
                 assert_eq!(sequences, vec![0, 1]);
@@ -1868,7 +1906,7 @@ mod tests {
             );
         }
 
-        match handle_query(&index, logs_query(Some("timestamp>2000"))) {
+        match handle_query(&index, logs_query(Some("timestamp>2000")), 0) {
             EngineResponse::Logs(entries) => {
                 let sequences: Vec<u64> = entries.iter().map(|e| e.sequence).collect();
                 assert_eq!(sequences, vec![3, 4]);
@@ -1898,6 +1936,7 @@ mod tests {
         match handle_query(
             &index,
             logs_query(Some(r#"regex("boom") and requests[level]==error"#)),
+            0,
         ) {
             EngineResponse::Logs(entries) => {
                 let sequences: Vec<u64> = entries.iter().map(|e| e.sequence).collect();
@@ -1910,6 +1949,7 @@ mod tests {
         match handle_query(
             &index,
             logs_query(Some(r#"regex("boom") or requests[level]==error"#)),
+            0,
         ) {
             EngineResponse::Logs(entries) => {
                 let sequences: Vec<u64> = entries.iter().map(|e| e.sequence).collect();
@@ -1926,7 +1966,7 @@ mod tests {
         ingest_log(&mut index, 0, "level=info hello");
         ingest_log(&mut index, 1, "no match here");
 
-        let EngineResponse::Logs(entries) = handle_query(&index, logs_query(None)) else {
+        let EngineResponse::Logs(entries) = handle_query(&index, logs_query(None), 0) else {
             panic!("expected Logs response");
         };
 
@@ -1945,7 +1985,7 @@ mod tests {
         ingest_log(&mut index, 1, "an error occurred");
         ingest_log(&mut index, 2, "another error here");
 
-        match handle_query(&index, timeline_query(Some(r#"regex("error")"#), 1_000_000)) {
+        match handle_query(&index, timeline_query(Some(r#"regex("error")"#), 1_000_000), 0) {
             EngineResponse::Timeline(buckets) => {
                 let total: u64 = buckets.iter().map(|b| b.count).sum();
                 assert_eq!(total, 2);
@@ -1959,12 +1999,12 @@ mod tests {
         let mut index = BTreeMap::new();
         ingest_log(&mut index, 0, "hello");
 
-        match handle_query(&index, logs_query(Some("@@@ not a valid filter @@@"))) {
+        match handle_query(&index, logs_query(Some("@@@ not a valid filter @@@")), 0) {
             EngineResponse::Error(message) => assert!(!message.is_empty()),
             _ => panic!("expected an Error response for a malformed filter string"),
         }
 
-        match handle_query(&index, timeline_query(Some("@@@ not a valid filter @@@"), 1000)) {
+        match handle_query(&index, timeline_query(Some("@@@ not a valid filter @@@"), 1000), 0) {
             EngineResponse::Error(message) => assert!(!message.is_empty()),
             _ => panic!("expected an Error response for a malformed filter string"),
         }
@@ -1984,7 +2024,7 @@ mod tests {
         .unwrap();
         ingest_log(&mut index, 0, "level=error");
 
-        match handle_query(&index, logs_query(Some("requests==5"))) {
+        match handle_query(&index, logs_query(Some("requests==5")), 0) {
             EngineResponse::Error(message) => assert!(message.contains("param")),
             _ => panic!("expected an Error response for a metric comparison without [param]"),
         }
diff --git a/webapp/src/components/NavMenu.tsx b/webapp/src/components/NavMenu.tsx
index c7bd83f..7618cad 100644
--- a/webapp/src/components/NavMenu.tsx
+++ b/webapp/src/components/NavMenu.tsx
@@ -87,6 +87,7 @@ export function NavMenu({ stats }: { stats: Stats | null }) {
               <div>
                 seq {stats.first_sequence ?? 0}–{stats.last_sequence ?? 0}
               </div>
+              <div>{stats.approx_bytes_total.toLocaleString()} bytes</div>
             </>
           ) : (
             <div>connecting…</div>
diff --git a/webapp/src/lib/api.ts b/webapp/src/lib/api.ts
index 63ead58..91c32ee 100644
--- a/webapp/src/lib/api.ts
+++ b/webapp/src/lib/api.ts
@@ -39,6 +39,8 @@ export interface Stats {
   last_sequence: number | null
   first_timestamp_ms: number | null
   last_timestamp_ms: number | null
+  /** Ticket 011: running approximate byte size of all currently-ingested logs. */
+  approx_bytes_total: number
 }
 
 export type ParamRole = 'label' | 'value'