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Health

Sleep Cycle Calculator

Find bedtime using 90-minute sleep cycles. Free online Sleep Cycle Calculator for health — instant, accurate results, mobile-friendly, no signup needed.

Bedtime hour
23.5

Derivation

  1. ├── 01Givenwake_hour = 7, cycles = 5
  2. ├── 02Formula(e.wake_hour-1.5 × e.cycles+24)%24
  3. ├── 03Substitute(e.7-1.5 × e.5+24)%24
  4. └── 04Compute Bedtime hour23.5
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§01What is

Understanding the Sleep Cycle Calculator

The Sleep Cycle Calculator computes Bedtime hour from 2 inputs: wake hour (0-23), cycles. Find bedtime using 90-minute sleep cycles.

Health metrics give us objective checkpoints against a body that can feel unreliable. Used alongside professional guidance — not in place of it — these numbers help you track progress and spot trends that matter. The Sleep Cycle Calculator sits in that toolkit — it find bedtime using 90-minute sleep cycles. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

(e.wake_hour-1.5 × e.cycles+24)%24

Where

wake_hour
Wake hour (0-23)
cycles
Cycles
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Wake hour (0-23) = 7, Cycles = 5.

  1. 01Start by noting the input — Wake hour (0-23): 7.
  2. 02Start by noting the input — Cycles: 5.
  3. 03Substitute these values into the formula: (e.wake_hour-1.5 × e.cycles+24)%24
  4. 04Compute Bedtime hour: the calculator returns 23.5.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Sleep Cycle Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Wake hour (0-23) halved

wake_hour = 3.5 (from 7)

Keep every other input at its default and halve the wake hour (0-23). See how bedtime hour responds.

  1. 01New Wake hour (0-23): 3.5
  2. 02Baseline Bedtime hour: 23.5
  3. 03New Bedtime hour: 20
  4. 04Bedtime hour decreases by 14.9% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Wake hour (0-23) doubled

wake_hour = 14 (from 7)

Keep every other input at its default and double the wake hour (0-23). See how bedtime hour responds.

  1. 01New Wake hour (0-23): 14
  2. 02Baseline Bedtime hour: 23.5
  3. 03New Bedtime hour: 6.5
  4. 04Bedtime hour decreases by 72.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Cycles halved

cycles = 2.5 (from 5)

Keep every other input at its default and halve the cycles. See how bedtime hour responds.

  1. 01New Cycles: 2.5
  2. 02Baseline Bedtime hour: 23.5
  3. 03New Bedtime hour: 3.25
  4. 04Bedtime hour decreases by 86.2% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Cycles doubled

cycles = 10 (from 5)

Keep every other input at its default and double the cycles. See how bedtime hour responds.

  1. 01New Cycles: 10
  2. 02Baseline Bedtime hour: 23.5
  3. 03New Bedtime hour: 16
  4. 04Bedtime hour decreases by 31.9% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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