Acceleration of a Particle in an Electric Field Calculator
Find the acceleration of a charged particle — such as a proton, electron, or ion — in a uniform electric field. Enter the charge in elementary charge units, the field strength in N/C (= V/m), and the particle mass in atomic mass units to get acceleration in m/s² along with the electric force and SI values.
e
N/C
u
Acceleration of the particle along the field direction (negative = opposes field)
- 1
Charge in coulombs
1 × 1.602×10⁻¹⁹ C = 0 CConvert elementary-charge units to SI coulombs. - 2
Mass in kilograms
1.007276 u × 1.661×10⁻²⁷ kg/u = 0 kg - 3
Electric force F = q × E
0 × 1,000 = 0 N - 4
Acceleration a = F ÷ m
0 ÷ 0 = 95,788,375,933.3621 m/s²
How does this calculator work?
A charged particle in a uniform electric field E experiences force F = qE and accelerates at a = qE/m. Enter charge in elementary charge units, field in N/C, and mass in atomic mass units. A proton in a 1000 N/C field accelerates at about 9.6 × 10¹⁰ m/s². Formula is non-relativistic.
Formula
How this is calculated
A uniform electric field E (in N/C or equivalently V/m) exerts a force F = qE on any charge q in the field. By Newton's second law, the resulting acceleration is a = F/m = qE/m. The direction of the acceleration matches the field direction for positive charges and opposes it for negative charges (such as electrons).
This calculator works with practical units: charge is given in multiples of the elementary charge e = 1.602 × 10⁻¹⁹ C (so a proton is +1, an electron is −1, an alpha particle is +2), and mass is given in atomic mass units u = 1.661 × 10⁻²⁷ kg (proton ≈ 1.0073 u, electron ≈ 0.000549 u). These are converted to SI internally before computing F and a.
The formula applies to a particle in free space under a uniform electrostatic field alone — it ignores magnetic fields, gravity (negligible for particles at these scales), radiation friction, and relativistic effects. For particles accelerated through a potential difference V, the kinetic energy gained is |q|V electron-volts; the motion eventually becomes relativistic at high energies (electrons at a few hundred keV, protons at a few hundred MeV), where this classical formula overestimates the speed.
Frequently asked questions
Both carry the same magnitude of charge, so they experience the same force F = eE. However, the electron is about 1836 times lighter than the proton, giving it 1836 times the acceleration a = F/m.
They are the same unit. Electric field in N/C (force per unit charge) equals V/m (potential gradient). Use whichever your textbook or equipment specifies.
No — at relativistic speeds (roughly >10% of c) classical mechanics underestimates inertia. Relativistic corrections replace m with γm, where γ = 1/√(1−v²/c²). This calculator is valid for non-relativistic speeds.
TG we-Calculate Editorial Team. (2026). Acceleration of a Particle in an Electric Field Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/acceleration-of-particle-in-electric-field-calculator
TG we-Calculate Editorial Team. "Acceleration of a Particle in an Electric Field Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/acceleration-of-particle-in-electric-field-calculator.
TG we-Calculate Editorial Team, "Acceleration of a Particle in an Electric Field Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/acceleration-of-particle-in-electric-field-calculator
@misc{wecalculate_acceleration_of_particle_in_electric_field_calculator, title = {Acceleration of a Particle in an Electric Field Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/acceleration-of-particle-in-electric-field-calculator}}, year = {2026}, note = {TG we-Calculate} }
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