Capacitive Sensor Change
C = ε0 × A / d
Quick answer
This calculator solves C = ε0 × A / d for Capacitance. With Permittivity (pF/m) 100 pF/m, Sensor Area 10 cm², Gap Distance 10 mm, the result is 10 pF. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Capacitive touch and proximity sensors detect changes in capacitance caused by the presence of a finger, hand, or other conductive object near the sensor electrode. The parallel plate capacitor model shows that capacitance increases with larger electrode area and decreases with greater distance. A human finger introduces a grounded conductor near the sensor pad, increasing the total capacitance by a few picofarads. Capacitive sensing ICs detect these tiny changes using charge transfer, sigma-delta, or relaxation oscillator measurement techniques.
Variables
- dC — Total electrode capacitance (F)
- ε0 — Permittivity of the gap medium (F/m), typically 8.854 pF/m for air
- A — Effective electrode area (m²)
- d — Distance between finger and electrode (m)
Practical Notes
Typical touch pad capacitance: 5-30 pF. A finger touch adds 1-5 pF. The sensing IC must detect changes of 0.1-1 pF reliably. Keep sensor traces short and away from noisy signals. Use a ground plane on the opposite side of the PCB from the sensor for better shielding. Moisture, temperature, and PCB contamination affect baseline capacitance, requiring auto-calibration.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| dC | Capacitance | pF | pF, nF, µF, mF, F |
| epsilon0 | Permittivity (pF/m) | pF/m | pF/m |
| A | Sensor Area | cm² | mm², cm², m² |
| d | Gap Distance | mm | mm |
Step by step
- 1. What you know: Permittivity (pF/m) 100 pF/m, Sensor Area 10 cm², Gap Distance 10 mm
- 2. The relation: C = ε0 × A / d
- 3. Substitute: epsilon0 = 100 pF/m, A = 10 cm², d = 10 mm
- 4. Result: Capacitance = 10 pF
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 10 pF | 0% |
| E24 | 10 pF | 0% |
Worked examples
Minimum range
Given: Permittivity (pF/m) 1 pF/m, Sensor Area 10 mm², Gap Distance 0.1 mm
Result: Capacitance = 0.1 pF
Low range
Given: Permittivity (pF/m) 10 pF/m, Sensor Area 1 cm², Gap Distance 1 mm
Result: Capacitance = 1 pF
Typical
Given: Permittivity (pF/m) 100 pF/m, Sensor Area 10 cm², Gap Distance 10 mm
Result: Capacitance = 10 pF
High range
Given: Permittivity (pF/m) 1000 pF/m, Sensor Area 100 cm², Gap Distance 100 mm
Result: Capacitance = 100 pF
Maximum range
Given: Permittivity (pF/m) 10000 pF/m, Sensor Area 0.1 m², Gap Distance 1000 mm
Result: Capacitance = 1 nF
Solving for each variable
Solve for Capacitance
Permittivity (pF/m) 1 pF/m, Sensor Area 10 mm², Gap Distance 0.1 mm → 0.1 pF
Solve for Permittivity (pF/m)
Capacitance 1 pF, Sensor Area 10 mm², Gap Distance 0.1 mm → 10 pF/m
Solve for Sensor Area
Capacitance 1 pF, Permittivity (pF/m) 1 pF/m, Gap Distance 0.1 mm → 1 cm²
Solve for Gap Distance
Capacitance 1 pF, Permittivity (pF/m) 1 pF/m, Sensor Area 10 mm² → 0.01 mm
How Capacitance changes with Permittivity (pF/m)
| Permittivity (pF/m) (input) | Capacitance (result) |
|---|---|
| 10 pF/m | 1 pF |
| 25 pF/m | 2.5 pF |
| 50 pF/m | 5 pF |
| 75 pF/m | 7.5 pF |
| 100 pF/m | 10 pF |
| 150 pF/m | 15 pF |
| 200 pF/m | 20 pF |
| 400 pF/m | 40 pF |
| 700 pF/m | 70 pF |
| 1000 pF/m | 100 pF |
The same result in other units
| Unit | Value |
|---|---|
| pF | 10 |
| nF | 0.01 |
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<p><a href="https://vbatpower.com/formulas/capacitive-touch/">Capacitive Sensor Change</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Capacitive Sensor Change?
Use C = ε0 × A / d. With Permittivity (pF/m) 100 pF/m, Sensor Area 10 cm², Gap Distance 10 mm, Capacitance works out to 10 pF.
What is the formula for Capacitive Sensor Change?
The formula is C = ε0 × A / d. Capacitive touch and proximity sensors detect changes in capacitance caused by the presence of a finger, hand, or other conductive object near the sensor electrode.
How do you find Permittivity (pF/m) when you know the other values?
Rearrange for Permittivity (pF/m): with Capacitance 1 pF, Sensor Area 10 mm², Gap Distance 0.1 mm, Permittivity (pF/m) is 10 pF/m.
How do you find Sensor Area when you know the other values?
Rearrange for Sensor Area: with Capacitance 1 pF, Permittivity (pF/m) 1 pF/m, Gap Distance 0.1 mm, Sensor Area is 1 cm².
What units does Capacitive Sensor Change use?
Capacitance is shown in pF, nF. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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