Buck-Boost Duty Cycle
D = Vout / (Vin + Vout)
Quick answer
This calculator solves D = V_out / (V_in + V_out) for Duty Cycle. With Output Voltage 12 V, Input Voltage 26.4 V, the result is 31.25 %. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The inverting buck-boost converter can produce an output voltage that is either higher or lower than the input, with inverted polarity. The duty cycle determines the output voltage magnitude. At D = 0.5, Vout = Vin. For D < 0.5, the converter acts like a buck (Vout < Vin). For D > 0.5, it acts like a boost (Vout > Vin). This topology is used when the input voltage range straddles the desired output voltage, such as single-cell Li-ion (2.7-4.2 V) powering a 3.3 V rail. The SEPIC and Ćuk converters share this same duty cycle relationship.
Variables
- D — Duty cycle (ratio 0 to 1)
- V_out — Output voltage magnitude (V)
- V_in — Input voltage (V)
Practical Notes
This is the ideal (lossless) relationship. Real converters have higher duty cycles due to switch, diode, and inductor losses. The formula assumes continuous conduction mode (CCM). In discontinuous conduction mode (DCM), the relationship changes and depends on load current. The same formula applies to SEPIC and Ćuk converter topologies.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| D | Duty Cycle | — | —, % |
| Vout | Output Voltage | V | pV, nV, µV, mV, V, kV |
| Vin | Input Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Output Voltage 12 V, Input Voltage 26.4 V
- 2. The relation: D = V_out / (V_in + V_out)
- 3. Substitute: Vout = 12 V, Vin = 26.4 V
- 4. Result: Duty Cycle = 31.25 %
Worked examples
Minimum range
Given: Output Voltage 0.33 V, Input Voltage 0.726 V
Result: Duty Cycle = 31.25 %
Low range
Given: Output Voltage 3.3 V, Input Voltage 7.26 V
Result: Duty Cycle = 31.25 %
Typical
Given: Output Voltage 12 V, Input Voltage 26.4 V
Result: Duty Cycle = 31.25 %
High range
Given: Output Voltage 0.23 kV, Input Voltage 0.506 kV
Result: Duty Cycle = 31.25 %
Maximum range
Given: Output Voltage 2.3 kV, Input Voltage 5.06 kV
Result: Duty Cycle = 31.25 %
Solving for each variable
Solve for Duty Cycle
Output Voltage 0.33 V, Input Voltage 0.726 V → 31.25 %
Solve for Output Voltage
Duty Cycle 2.5 %, Input Voltage 0.726 V → 18.62 mV
Solve for Input Voltage
Duty Cycle 2.5 %, Output Voltage 0.33 V → 12.87 V
How Duty Cycle changes with Output Voltage
| Output Voltage (input) | Duty Cycle (result) |
|---|---|
| 1.2 V | 4.348 % |
| 3 V | 10.2 % |
| 6 V | 18.52 % |
| 9 V | 25.42 % |
| 12 V | 31.25 % |
| 18 V | 40.54 % |
| 24 V | 47.62 % |
| 48 V | 0.6452 |
| 84 V | 0.7609 |
| 120 V | 0.8197 |
The same result in other units
| Unit | Value |
|---|---|
| 0.3125 | |
| % | 31.25 |
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<p><a href="https://vbatpower.com/formulas/buck-boost-duty/">Buck-Boost Duty Cycle</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Buck-Boost Duty Cycle?
Use D = V_out / (V_in + V_out). With Output Voltage 12 V, Input Voltage 26.4 V, Duty Cycle works out to 31.25 %.
What is the formula for Buck-Boost Duty Cycle?
The formula is D = V_out / (V_in + V_out). The inverting buck-boost converter can produce an output voltage that is either higher or lower than the input, with inverted polarity.
How do you find Output Voltage when you know the other values?
Rearrange for Output Voltage: with Duty Cycle 2.5 %, Input Voltage 0.726 V, Output Voltage is 18.62 mV.
How do you find Input Voltage when you know the other values?
Rearrange for Input Voltage: with Duty Cycle 2.5 %, Output Voltage 0.33 V, Input Voltage is 12.87 V.
What units does Buck-Boost Duty Cycle use?
Duty Cycle is shown in , %. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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