Formulas

1. Error Rate

Measures the proportion of "bad" events relative to total events over a period.

Formula: Error Rate = Bad Events / Total Events

Usage: Used to determine the amount of time or budget burned during a specific window.

2. Burn Rate

Measures how fast you are consuming your error budget relative to the allowed rate based on your SLO period. A burn rate of 1 means you're consuming budget exactly on track; higher numbers mean faster consumption.

Formula: Burn Rate = Observed Error Rate / (1 - SLO Target)

Where:

  • Observed Error Rate: Actual error rate measured (e.g., 0.1 for 10%).
  • SLO Target: Target service level objective (e.g., 0.99 for 99%).
  • (1 - SLO Target): Total Error Budget expressed as a percentage (e.g., 0.01 for 1%).

Example:

  • Observed Error Rate = 10% (0.1)
  • SLO Target = 99% (0.99)
  • Calculation:
    Burn Rate = 0.1 / (1 - 0.99) = 0.1 / 0.01 = 10
  • Interpretation: You are burning through your budget 10x faster than allowed over the SLO period.

3. Budget Consumed During Alerting Window (%)

Calculates what percentage of your total error budget (for the entire SLO period) is consumed if the observed burn rate persists for the duration of your alerting window.

Formula:
% Budget Consumed = Burn Rate * (Alerting Window Duration / SLO Period Duration) * 100

Where:

  • Burn Rate: As calculated above.
  • Alerting Window Duration: Duration your alert evaluates (e.g., 60 minutes).
  • SLO Period Duration: Full SLO period (e.g., 43,200 minutes for 30 days).

⚠️ Make sure units match between Alerting Window and SLO Period!

Example:

  • Burn Rate = 10
  • Alerting Window = 60 minutes
  • SLO Period = 30 days (43,200 minutes)
  • Calculation:
    % Budget Consumed = 10 * (60 / 43200) * 100 = 1.388%
  • Interpretation: If a burn rate of 10 persists for 60 minutes, 1.39% of the 30-day error budget is consumed.

Calculating Time Burned from %:

  • Total Budget Time = 432 minutes (for 99% SLO over 30 days)
  • Time Burned = Total Budget Time * (% Budget Consumed / 100)
  • Example:
    Time Burned = 432 * 0.01388 = 6 minutes

💡 Note:
Substituting the burn rate formula gives:
(Observed Error Rate / Total Error Budget %) * (Alerting Window Duration / SLO Period Duration) * 100
This connects the observed error rate to budget consumption over time.

4. Required Burn Rate for Theoretical Budget Consumption

Calculates the Burn Rate you should alert on to catch a certain % of error budget burned within an alerting window. (Rearranges Formula #3.)

This answers: "How fast am I burning if I consume X% of my budget within Y window?"

Formula:
Required Burn Rate = (% Budget To Consume / 100) * (SLO Period Duration / Alerting Window Duration)

Where:

  • % Budget To Consume: Desired % of budget to trigger an alert (e.g., 2%).
  • SLO Period Duration: Full SLO measurement period.
  • Alerting Window Duration: Time window for the alert.

Key Concepts:

  • The "ideal" percentage to burn per window is 1 / (number of windows).
  • Anything over that is a multiplier relative to ideal consumption.

Example (7-Day SLO):

  • Goal: Alert when 10% of budget is consumed within 1 hour.
  • SLO Period = 7 days × 24 hours = 168 hours
  • Alerting Window = 1 hour
  • Calculation:
    Required Burn Rate = (10 / 100) * (168 / 1) = 16.8
  • Interpretation: Set an alert to fire if burn rate exceeds 16.8 over a 1-hour window.

Example Walkthrough (7-Day SLO, 99% Target):

  • SLO Target = 99% ➔ Error Budget = 1% (0.01)
  • SLO Period = 168 hours
  • Total Budget Time = 0.01 * 168 = 1.68 hours
  • Goal: Alert if 10% of 1.68 hours = 0.168 hours are consumed in 1 hour.
  • Observed Error Rate needed:
    0.168 / 1 = 0.168 (16.8%)
  • Checking Required Burn Rate:
    0.168 / 0.01 = 16.8 — matches!

Calculation Examples

Scenario Setup

  • SLO Target: 99% (Error Budget = 1% or 0.01)
  • SLO Period: 30 days (43,200 minutes)
  • Total Error Budget Time: 0.01 * 43200 = 432 minutes
  • Alerting Window: 60 minutes

Example 1: High Error Rate (3%)

  • Observed Error Rate = 3% (0.03)
  • Time Burned in Window: 0.03 * 60 = 1.8 minutes
  • % Budget Burned in Window: (1.8 / 432) * 100 = 0.416%
  • Burn Rate: 0.03 / 0.01 = 3
  • Verify with Burn Rate:
    3 * (60 / 43200) * 100 = 0.416% (Matches!)

Interpretation:
An error rate of 3% leads to a burn rate of 3. We consume 1.8 minutes (0.42%) of the total monthly budget in that hour.

Example 2: Steady Low Error Rate (0.01%)

  • Observed Error Rate = 0.01% (0.0001)
  • Time Burned in Window: 0.0001 * 60 = 0.006 minutes
  • Burn Rate: 0.0001 / 0.01 = 0.01
  • Verify with Burn Rate:
    0.01 * (60 / 43200) * 100 = 0.00139%

Interpretation:
A very low error rate results in a negligible burn rate (<1) and minimal budget consumption.

Example 3: Sustained High Error Rate (10%) — How Long Until Budget Depleted?

  • Observed Error Rate = 10% (0.1)
  • Burn Rate: 0.1 / 0.01 = 10
  • Time to Deplete Budget:
    SLO Period Duration / Burn Rate
  • Calculations:
    30 days / 10 = 3 days
    or
    43200 minutes / 10 = 4320 minutes = 72 hours = 3 days

Interpretation:
A 10% sustained error rate would deplete the entire 30-day budget in just 3 days.

Example 4: Using Required Burn Rate Method

  • Goal: How fast to burn 10% of budget in 10 hours?
  • Calculation:
    Required Burn Rate = (10 / 100) * (43200 / 600) = 0.1 * 72 = 7.2

Interpretation:
A burn rate of 7.2 would burn 10% of the monthly budget over a 10-hour window.