Dielectric Dissipation Factor
DF = ESR × 2πfC
Quick answer
This calculator solves DF = ESR × ω × C = tan(δ) for Dissipation Factor. With ESR 50 mΩ, Frequency 100 kHz, Capacitance 100 µF, the result is 3.142. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The dissipation factor (DF), also called tan δ (loss tangent), quantifies the ratio of energy lost to energy stored per cycle in a capacitor. It equals ESR divided by the capacitive reactance: DF = ESR / Xc = ESR × ωC. A lower DF indicates a more ideal capacitor. C0G/NP0 ceramics have DF < 0.001 (0.1%), X7R ceramics have DF around 0.025 (2.5%), and aluminum electrolytics can exceed 0.1 (10%). DF is frequency-dependent and generally increases with frequency and temperature.
Variables
- DF — Dissipation factor, also tan δ (dimensionless)
- ESR — Equivalent series resistance (Ω)
- f — Measurement frequency (Hz)
- C — Capacitance (F)
Practical Notes
Quality factor Q = 1/DF. Capacitor datasheets specify DF at a standard test frequency (typically 120 Hz for electrolytics, 1 kHz or 1 MHz for ceramics). For resonant circuits and RF applications, use capacitors with the lowest possible DF. Film capacitors (polypropylene, polystyrene) offer very low DF, making them ideal for audio and RF applications.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| DF | Dissipation Factor | — | — |
| ESR | ESR | mΩ | mΩ, Ω, kΩ, MΩ |
| f | Frequency | kHz | Hz, kHz, MHz, GHz |
| C | Capacitance | µF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: ESR 50 mΩ, Frequency 100 kHz, Capacitance 100 µF
- 2. The relation: DF = ESR × ω × C = tan(δ)
- 3. Substitute: ESR = 50 mΩ, f = 100 kHz, C = 100 µF
- 4. Result: Dissipation Factor = 3.142
Worked examples
Minimum range
Given: ESR 0.1 mΩ, Frequency 100 Hz, Capacitance 100 nF
Result: Dissipation Factor = 6.28 × 10⁻⁹
Low range
Given: ESR 1 mΩ, Frequency 1 kHz, Capacitance 1 µF
Result: Dissipation Factor = 6.28 × 10⁻⁶
Typical
Given: ESR 50 mΩ, Frequency 100 kHz, Capacitance 100 µF
Result: Dissipation Factor = 3.142
High range
Given: ESR 0.5 Ω, Frequency 0.5 MHz, Capacitance 1 mF
Result: Dissipation Factor = 1571
Maximum range
Given: ESR 5 Ω, Frequency 5 MHz, Capacitance 10 mF
Result: Dissipation Factor = 1.57 × 10⁶
Solving for each variable
Solve for Dissipation Factor
ESR 0.1 mΩ, Frequency 100 Hz, Capacitance 100 nF → 6.28 × 10⁻⁹
Solve for ESR
Dissipation Factor 0.025, Frequency 100 Hz, Capacitance 100 nF → 0.3979 kΩ
How Dissipation Factor changes with ESR
| ESR (input) | Dissipation Factor (result) |
|---|---|
| 5 mΩ | 0.3142 |
| 12.5 mΩ | 0.7854 |
| 25 mΩ | 1.571 |
| 37.5 mΩ | 2.356 |
| 50 mΩ | 3.142 |
| 75 mΩ | 4.712 |
| 100 mΩ | 6.283 |
| 0.2 Ω | 12.57 |
| 0.35 Ω | 21.99 |
| 0.5 Ω | 31.42 |
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<p><a href="https://vbatpower.com/formulas/dielectric-loss-factor/">Dielectric Dissipation Factor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Dielectric Dissipation Factor?
Use DF = ESR × ω × C = tan(δ). With ESR 50 mΩ, Frequency 100 kHz, Capacitance 100 µF, Dissipation Factor works out to 3.142.
What is the formula for Dielectric Dissipation Factor?
The formula is DF = ESR × ω × C = tan(δ). The dissipation factor (DF), also called tan δ (loss tangent), quantifies the ratio of energy lost to energy stored per cycle in a capacitor.
How do you find ESR when you know the other values?
Rearrange for ESR: with Dissipation Factor 0.025, Frequency 100 Hz, Capacitance 100 nF, ESR is 0.3979 kΩ.
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