Calculate force, charge, distance, or Coulomb’s constant with Coulomb’s law by entering four known values in common units and choosing units.
Customize This Calculator
Build your own version. Describe what you want changed, added, or compared.
- All Physics Calculators
- Coulomb’s Law Calculator
- Coulombs To Newtons Calculator
- Coulombs To Joules Calculator
Coulomb’s Constant Formula
The calculator is based on Coulomb’s law. It uses SI base units internally: newtons for force, coulombs for charge, meters for distance, and N·m²/C² for Coulomb’s constant.
- F = electrostatic force between the two charges
- k = Coulomb’s constant
- q1 = first electric charge
- q2 = second electric charge
- r = distance between the charges
To use the calculator, enter any four of the five values. The missing value is found by rearranging Coulomb’s law.
- Force: Uses the two charges, distance, and Coulomb’s constant to find the magnitude of the electrostatic force.
- Charge 1 or Charge 2: Rearranges Coulomb’s law to find the missing charge when the force, other charge, distance, and constant are known.
- Distance: Solves for the separation distance needed to produce the given force between two charges.
- Coulomb’s Constant: Solves for k from force, charge, and distance values. In a vacuum, k is normally about 8.98755 × 109 N·m²/C².
Common Values and Unit Conversions
Use these values to check that your inputs are in the expected range and unit system.
| Quantity | Value | Notes |
|---|---|---|
| Coulomb’s constant in vacuum | 8.9875517923 × 109 N·m²/C² | Often rounded to 8.99 × 109 |
| Coulomb’s constant in lbf·ft²/C² | 6.629 × 109 lbf·ft²/C² | Approximate imperial-force form |
| Elementary charge | 1.602176634 × 10-19 C | Charge of one proton in magnitude |
| Unit | Equivalent in base units | Used for |
|---|---|---|
| 1 lbf | 4.44822 N | Force |
| 1 mC | 0.001 C | Charge |
| 1 μC | 0.000001 C | Charge |
| 1 cm | 0.01 m | Distance |
| 1 in | 0.0254 m | Distance |
| 1 ft | 0.3048 m | Distance |
Example Calculations
Example 1: Calculate force
Find the force between two charges of 2 μC and 3 μC separated by 0.5 m. Use k = 8.98755 × 109 N·m²/C².
Convert the charges to coulombs:
2 μC = 0.000002 C and 3 μC = 0.000003 C
Apply Coulomb’s law:
F = 8.98755 × 109 × |0.000002 × 0.000003| / 0.52
F = 0.215701 N
Example 2: Calculate distance
Two charges are 5 μC and 4 μC. The force between them is 2 N. Use k = 8.98755 × 109 N·m²/C².
Convert the charges to coulombs:
5 μC = 0.000005 C and 4 μC = 0.000004 C
Apply the distance formula:
r = sqrt((8.98755 × 109 × |0.000005 × 0.000004|) / 2)
r = 0.299792 m
FAQ
What value should I enter for Coulomb’s constant?
For most physics problems in air or vacuum, enter 8.98755 × 109 N·m²/C². Many textbooks round this to 9.0 × 109 N·m²/C². If your problem gives a specific value for k, use the value from the problem.
Why does the calculator use the absolute value of the charges for force?
The calculator gives the magnitude of the electrostatic force. Magnitude is positive. The signs of the charges tell you the direction of the force: like charges repel, and opposite charges attract.
Can Coulomb’s law be used for any charged objects?
Coulomb’s law works best for point charges or objects that can be treated like point charges. For large charged objects, irregular shapes, or charges spread over a surface, the simple two-charge formula may not be enough without additional physics methods.
