Battery Voltage Sag
Vsag = Voc − Crate × Q × Rint
Quick answer
This calculator solves V_sag = V_oc − C_rate × Q × R_int for Vsag. With Open-Circuit Voltage 12 V, C-Rate 0.5, Battery Capacity 2.5 Ah, Internal Resistance 50 mΩ, the result is 11.94.
Calculator
Formula
Description
Voltage sag is the drop in battery terminal voltage under load, caused by current flowing through the internal resistance. Combining the C-rate concept with the internal resistance model: since I = Crate × Q, the voltage drop is Crate × Q × Rint. This is critical for determining whether a battery can maintain the minimum operating voltage of the load at the required current. High-drain applications (power tools, drones, EVs) require low-impedance cells to minimize sag. Voltage sag is worst at low SoC and low temperature when internal resistance is highest.
Variables
- V_oc — Open-circuit voltage at current SoC (V)
- C_rate — Discharge C-rate (dimensionless)
- Q — Battery capacity (Ah)
- R_int — Internal resistance (Ω)
Practical Notes
Example: A 3.7 V, 3 Ah cell with 50 mΩ internal resistance at 3C: Vsag = 3.7 − 3 × 3 × 0.05 = 3.7 − 0.45 = 3.25 V. If the load cutoff is 3.0 V, this leaves only 0.25 V margin. At 5C (15 A), the sag would be 0.75 V, dropping to 2.95 V — below cutoff. This calculation is essential for selecting cells that can support the required discharge rates.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Voc | Open-Circuit Voltage | V | pV, nV, µV, mV, V, kV |
| Crate | C-Rate | — | — |
| Q | Battery Capacity | mAh | mAh, Ah |
| Rint | Internal Resistance | mΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Open-Circuit Voltage 12 V, C-Rate 0.5, Battery Capacity 2.5 Ah, Internal Resistance 50 mΩ
- 2. The relation: V_sag = V_oc − C_rate × Q × R_int
- 3. Substitute: Voc = 12 V, Crate = 0.5, Q = 2.5 Ah, Rint = 50 mΩ
- 4. Result: Vsag = 11.94
Related quantities from the same inputs
- P = V² / R = 2.88 kW
- I = V / R = 240 A
Worked examples
Minimum range
Given: Open-Circuit Voltage 0.33 V, C-Rate 0.025, Battery Capacity 50 mAh, Internal Resistance 0.1 mΩ
Result: Vsag = 0.33
Low range
Given: Open-Circuit Voltage 3.3 V, C-Rate 0.25, Battery Capacity 0.5 Ah, Internal Resistance 1 mΩ
Result: Vsag = 3.3
Typical
Given: Open-Circuit Voltage 12 V, C-Rate 0.5, Battery Capacity 2.5 Ah, Internal Resistance 50 mΩ
Result: Vsag = 11.94
High range
Given: Open-Circuit Voltage 0.23 kV, C-Rate 0.8, Battery Capacity 10 Ah, Internal Resistance 0.5 Ω
Result: Vsag = 226
Maximum range
Given: Open-Circuit Voltage 2.3 kV, C-Rate 8, Battery Capacity 100 Ah, Internal Resistance 5 Ω
Result: Vsag = -1700
How Vsag changes with Open-Circuit Voltage
| Open-Circuit Voltage (input) | Vsag (result) |
|---|---|
| 1.2 V | 1.138 |
| 3 V | 2.938 |
| 6 V | 5.938 |
| 9 V | 8.938 |
| 12 V | 11.94 |
| 18 V | 17.94 |
| 24 V | 23.94 |
| 48 V | 47.94 |
| 84 V | 83.94 |
| 120 V | 119.9 |
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<p><a href="https://vbatpower.com/formulas/battery-impedance-sag/">Battery Voltage Sag</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Battery Voltage Sag?
Use V_sag = V_oc − C_rate × Q × R_int. With Open-Circuit Voltage 12 V, C-Rate 0.5, Battery Capacity 2.5 Ah, Internal Resistance 50 mΩ, Vsag works out to 11.94.
What is the formula for Battery Voltage Sag?
The formula is V_sag = V_oc − C_rate × Q × R_int. Voltage sag is the drop in battery terminal voltage under load, caused by current flowing through the internal resistance.
Related Concepts
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