diff --git a/crates/common/src/retry/backoff.rs b/crates/common/src/retry/backoff.rs
new file mode 100644
index 00000000..97e9841f
--- /dev/null
+++ b/crates/common/src/retry/backoff.rs
@@ -0,0 +1,510 @@
+use std::time::Duration;
+
+use rand::Rng;
+
+use crate::configuration::{extract_provider, BackoffApplyTo, BackoffConfig, RetryStrategy};
+
+/// Calculator for exponential backoff delays with jitter and scope filtering.
+pub struct BackoffCalculator;
+
+impl BackoffCalculator {
+    /// Calculate the delay before the next retry attempt.
+    ///
+    /// Returns the greater of the computed backoff delay and the Retry-After delay.
+    /// Returns zero when the backoff `apply_to` scope doesn't match the
+    /// current/previous provider relationship (unless retry_after_seconds is set).
+    pub fn calculate_delay(
+        &self,
+        attempt_number: u32,
+        backoff_config: Option<&BackoffConfig>,
+        retry_after_seconds: Option<u64>,
+        current_strategy: RetryStrategy,
+        current_provider: &str,
+        previous_provider: &str,
+    ) -> Duration {
+        let backoff_delay = match backoff_config {
+            Some(config) => {
+                if !Self::scope_matches(
+                    config.apply_to,
+                    current_strategy,
+                    current_provider,
+                    previous_provider,
+                ) {
+                    Duration::ZERO
+                } else {
+                    Self::compute_backoff(attempt_number, config)
+                }
+            }
+            None => Duration::ZERO,
+        };
+
+        let retry_after_delay = retry_after_seconds
+            .map(|s| Duration::from_secs(s))
+            .unwrap_or(Duration::ZERO);
+
+        backoff_delay.max(retry_after_delay)
+    }
+
+    /// Check whether the backoff `apply_to` scope matches the current retry context.
+    fn scope_matches(
+        apply_to: BackoffApplyTo,
+        _current_strategy: RetryStrategy,
+        current_provider: &str,
+        previous_provider: &str,
+    ) -> bool {
+        let current_prefix = extract_provider(current_provider);
+        let previous_prefix = extract_provider(previous_provider);
+
+        match apply_to {
+            BackoffApplyTo::SameModel => current_provider == previous_provider,
+            BackoffApplyTo::SameProvider => current_prefix == previous_prefix,
+            BackoffApplyTo::Global => true,
+        }
+    }
+
+    /// Compute exponential backoff: min(base_ms * 2^attempt, max_ms), with optional jitter.
+    fn compute_backoff(attempt_number: u32, config: &BackoffConfig) -> Duration {
+        let exp_delay = if attempt_number >= 64 {
+            config.max_ms
+        } else {
+            config.base_ms.saturating_mul(1u64 << attempt_number)
+        };
+        let capped = exp_delay.min(config.max_ms);
+
+        let final_ms = if config.jitter {
+            let mut rng = rand::thread_rng();
+            let jitter_factor: f64 = 0.5 + rng.gen::<f64>() * 0.5;
+            ((capped as f64) * jitter_factor) as u64
+        } else {
+            capped
+        };
+
+        Duration::from_millis(final_ms)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::configuration::{BackoffApplyTo, BackoffConfig, RetryStrategy};
+    use proptest::prelude::*;
+
+    fn make_config(
+        apply_to: BackoffApplyTo,
+        base_ms: u64,
+        max_ms: u64,
+        jitter: bool,
+    ) -> BackoffConfig {
+        BackoffConfig {
+            apply_to,
+            base_ms,
+            max_ms,
+            jitter,
+        }
+    }
+
+    #[test]
+    fn no_backoff_config_returns_zero() {
+        let calc = BackoffCalculator;
+        let d = calc.calculate_delay(
+            0,
+            None,
+            None,
+            RetryStrategy::SameModel,
+            "openai/gpt-4o",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::ZERO);
+    }
+
+    #[test]
+    fn no_backoff_config_with_retry_after() {
+        let calc = BackoffCalculator;
+        let d = calc.calculate_delay(
+            0,
+            None,
+            Some(5),
+            RetryStrategy::SameModel,
+            "openai/gpt-4o",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_secs(5));
+    }
+
+    #[test]
+    fn exponential_backoff_no_jitter() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::Global, 100, 5000, false);
+
+        // attempt 0: min(100 * 2^0, 5000) = 100
+        assert_eq!(
+            calc.calculate_delay(0, Some(&config), None, RetryStrategy::SameModel, "a", "a"),
+            Duration::from_millis(100)
+        );
+        // attempt 1: min(100 * 2^1, 5000) = 200
+        assert_eq!(
+            calc.calculate_delay(1, Some(&config), None, RetryStrategy::SameModel, "a", "a"),
+            Duration::from_millis(200)
+        );
+        // attempt 2: min(100 * 2^2, 5000) = 400
+        assert_eq!(
+            calc.calculate_delay(2, Some(&config), None, RetryStrategy::SameModel, "a", "a"),
+            Duration::from_millis(400)
+        );
+        // attempt 6: min(100 * 64, 5000) = 5000 (capped)
+        assert_eq!(
+            calc.calculate_delay(6, Some(&config), None, RetryStrategy::SameModel, "a", "a"),
+            Duration::from_millis(5000)
+        );
+    }
+
+    #[test]
+    fn jitter_stays_within_bounds() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::Global, 1000, 50000, true);
+
+        for attempt in 0..5 {
+            for _ in 0..20 {
+                let d = calc.calculate_delay(
+                    attempt,
+                    Some(&config),
+                    None,
+                    RetryStrategy::SameModel,
+                    "a",
+                    "a",
+                );
+                let base = (1000u64.saturating_mul(1u64 << attempt)).min(50000);
+                // jitter: delay * (0.5 + random(0, 0.5)) => [0.5*base, 1.0*base]
+                assert!(
+                    d.as_millis() >= (base as f64 * 0.5) as u128,
+                    "delay {} too low for base {}",
+                    d.as_millis(),
+                    base
+                );
+                assert!(
+                    d.as_millis() <= base as u128,
+                    "delay {} too high for base {}",
+                    d.as_millis(),
+                    base
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn scope_same_model_filters_different_providers() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::SameModel, 100, 5000, false);
+
+        // Same model -> backoff applies
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::SameModel,
+            "openai/gpt-4o",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_millis(100));
+
+        // Different model, same provider -> no backoff
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::SameProvider,
+            "openai/gpt-4o-mini",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::ZERO);
+
+        // Different provider -> no backoff
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::DifferentProvider,
+            "anthropic/claude",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::ZERO);
+    }
+
+    #[test]
+    fn scope_same_provider_filters_different_providers() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::SameProvider, 100, 5000, false);
+
+        // Same provider -> backoff applies
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::SameProvider,
+            "openai/gpt-4o-mini",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_millis(100));
+
+        // Same model (same provider) -> backoff applies
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::SameModel,
+            "openai/gpt-4o",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_millis(100));
+
+        // Different provider -> no backoff
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::DifferentProvider,
+            "anthropic/claude",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::ZERO);
+    }
+
+    #[test]
+    fn scope_global_always_applies() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::Global, 100, 5000, false);
+
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            None,
+            RetryStrategy::DifferentProvider,
+            "anthropic/claude",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_millis(100));
+    }
+
+    #[test]
+    fn retry_after_wins_when_greater() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::Global, 100, 5000, false);
+
+        // retry_after = 10s >> backoff attempt 0 = 100ms
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            Some(10),
+            RetryStrategy::SameModel,
+            "a",
+            "a",
+        );
+        assert_eq!(d, Duration::from_secs(10));
+    }
+
+    #[test]
+    fn backoff_wins_when_greater() {
+        let calc = BackoffCalculator;
+        // base_ms=10000, attempt 0 -> 10000ms = 10s
+        let config = make_config(BackoffApplyTo::Global, 10000, 50000, false);
+
+        // retry_after = 5s < backoff = 10s
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            Some(5),
+            RetryStrategy::SameModel,
+            "a",
+            "a",
+        );
+        assert_eq!(d, Duration::from_millis(10000));
+    }
+
+    #[test]
+    fn scope_mismatch_still_honors_retry_after() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::SameModel, 100, 5000, false);
+
+        // Scope doesn't match (different providers) but retry_after is set
+        let d = calc.calculate_delay(
+            0,
+            Some(&config),
+            Some(3),
+            RetryStrategy::DifferentProvider,
+            "anthropic/claude",
+            "openai/gpt-4o",
+        );
+        assert_eq!(d, Duration::from_secs(3));
+    }
+
+    #[test]
+    fn large_attempt_number_saturates() {
+        let calc = BackoffCalculator;
+        let config = make_config(BackoffApplyTo::Global, 100, 5000, false);
+
+        // Very large attempt number should saturate and cap at max_ms
+        let d = calc.calculate_delay(63, Some(&config), None, RetryStrategy::SameModel, "a", "a");
+        assert_eq!(d, Duration::from_millis(5000));
+    }
+
+    // --- Proptest strategies ---
+
+    fn arb_provider() -> impl Strategy<Value = String> {
+        prop_oneof![
+            Just("openai/gpt-4o".to_string()),
+            Just("openai/gpt-4o-mini".to_string()),
+            Just("anthropic/claude-3".to_string()),
+            Just("azure/gpt-4o".to_string()),
+            Just("google/gemini-pro".to_string()),
+        ]
+    }
+
+    // Feature: retry-on-ratelimit, Property 12: Exponential Backoff Formula and Bounds
+    // **Validates: Requirements 4.6, 4.7, 4.8, 4.9, 4.10, 4.11**
+    proptest! {
+        #![proptest_config(ProptestConfig::with_cases(100))]
+
+        /// Property 12 – Case 1: No-jitter delay equals min(base_ms * 2^attempt, max_ms) exactly.
+        #[test]
+        fn prop_backoff_no_jitter_exact(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+        ) {
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::Global, base_ms, max_ms, false);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(attempt, Some(&config), None, RetryStrategy::SameModel, "a", "a");
+
+            let expected = if attempt >= 64 {
+                max_ms
+            } else {
+                base_ms.saturating_mul(1u64 << attempt).min(max_ms)
+            };
+            prop_assert_eq!(d, Duration::from_millis(expected));
+        }
+
+        /// Property 12 – Case 2: Jitter delay is in [0.5 * computed_base, computed_base].
+        #[test]
+        fn prop_backoff_jitter_bounds(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+        ) {
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::Global, base_ms, max_ms, true);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(attempt, Some(&config), None, RetryStrategy::SameModel, "a", "a");
+
+            let computed_base = if attempt >= 64 {
+                max_ms
+            } else {
+                base_ms.saturating_mul(1u64 << attempt).min(max_ms)
+            };
+            let lower = (computed_base as f64 * 0.5) as u64;
+            let upper = computed_base;
+            prop_assert!(
+                d.as_millis() >= lower as u128 && d.as_millis() <= upper as u128,
+                "delay {}ms not in [{}, {}] for attempt={}, base_ms={}, max_ms={}",
+                d.as_millis(), lower, upper, attempt, base_ms, max_ms
+            );
+        }
+
+        /// Property 12 – Case 3: Delay is always <= max_ms.
+        #[test]
+        fn prop_backoff_delay_capped_at_max(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+            jitter in proptest::bool::ANY,
+        ) {
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::Global, base_ms, max_ms, jitter);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(attempt, Some(&config), None, RetryStrategy::SameModel, "a", "a");
+
+            prop_assert!(
+                d.as_millis() <= max_ms as u128,
+                "delay {}ms exceeds max_ms {} for attempt={}, base_ms={}, jitter={}",
+                d.as_millis(), max_ms, attempt, base_ms, jitter
+            );
+        }
+    }
+
+    // Feature: retry-on-ratelimit, Property 13: Backoff Apply-To Scope Filtering
+    // **Validates: Requirements 4.3, 4.4, 4.5, 4.12, 4.13**
+    proptest! {
+        #![proptest_config(ProptestConfig::with_cases(100))]
+
+        /// Property 13 – Case 1: SameModel apply_to with different providers → zero delay.
+        #[test]
+        fn prop_scope_same_model_different_providers_zero(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+            current in arb_provider(),
+            previous in arb_provider(),
+        ) {
+            // Only test when providers are actually different models
+            prop_assume!(current != previous);
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::SameModel, base_ms, max_ms, false);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(
+                attempt, Some(&config), None,
+                RetryStrategy::DifferentProvider, &current, &previous,
+            );
+            prop_assert_eq!(d, Duration::ZERO,
+                "Expected zero delay for SameModel apply_to with different models: {} vs {}",
+                current, previous
+            );
+        }
+
+        /// Property 13 – Case 2: SameProvider apply_to with different provider prefixes → zero delay.
+        #[test]
+        fn prop_scope_same_provider_different_prefix_zero(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+            current in arb_provider(),
+            previous in arb_provider(),
+        ) {
+            let current_prefix = extract_provider(&current);
+            let previous_prefix = extract_provider(&previous);
+            prop_assume!(current_prefix != previous_prefix);
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::SameProvider, base_ms, max_ms, false);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(
+                attempt, Some(&config), None,
+                RetryStrategy::DifferentProvider, &current, &previous,
+            );
+            prop_assert_eq!(d, Duration::ZERO,
+                "Expected zero delay for SameProvider apply_to with different prefixes: {} vs {}",
+                current_prefix, previous_prefix
+            );
+        }
+
+        /// Property 13 – Case 3: Global apply_to always produces non-zero delay.
+        #[test]
+        fn prop_scope_global_always_nonzero(
+            attempt in 0u32..20,
+            base_ms in 1u64..10000,
+            extra in 1u64..40001u64,
+            current in arb_provider(),
+            previous in arb_provider(),
+        ) {
+            let max_ms = base_ms + extra;
+            let config = make_config(BackoffApplyTo::Global, base_ms, max_ms, false);
+            let calc = BackoffCalculator;
+            let d = calc.calculate_delay(
+                attempt, Some(&config), None,
+                RetryStrategy::DifferentProvider, &current, &previous,
+            );
+            prop_assert!(d > Duration::ZERO,
+                "Expected non-zero delay for Global apply_to: current={}, previous={}",
+                current, previous
+            );
+        }
+    }
+}