Calculator Inputs
Recent Calculation History
The table stores the latest twenty calculations in your session for quick review and export.
| Date | Particle | Method | m/q (kg/C) | q/m (C/kg) |
|---|---|---|---|---|
| No calculations saved yet. | ||||
Example Data Table
These example rows show typical particles and their mass-to-charge behavior using direct input values.
| Sample | Method | Given Inputs | m/q (kg/C) | q/m (C/kg) |
|---|---|---|---|---|
| Electron | Direct | m = 9.109e-31 kg, q = -1e | -5.685630e-12 | -1.758820e+11 |
| Proton | Direct | m = 1.673e-27 kg, q = +1e | 1.043968e-8 | 9.578833e+7 |
| Alpha Particle | Direct | m = 6.645e-27 kg, q = +2e | 2.073634e-8 | 4.822451e+7 |
| Sodium Ion (Na+) | Direct | m = 22.98976928 u, q = +1e | 2.382722e-7 | 4.196881e+6 |
Formula Used
1) Direct Method
Mass-to-charge ratio: m/q = m ÷ q
Charge-to-mass ratio: q/m = q ÷ m
2) Magnetic Field, Radius, and Velocity Method
From circular magnetic motion: qvB = mv²/r
Mass-to-charge ratio: m/q = Br ÷ v
3) Accelerating Voltage Method
Using qV = ½mv² and qvB = mv²/r
Mass-to-charge ratio: m/q = B²r² ÷ 2V
Use SI units for the cleanest interpretation: kilograms, coulombs, tesla, meters, meters per second, and volts. The calculator converts supported units automatically before applying each formula.
How to Use This Calculator
- Choose the calculation method that matches your available data.
- Enter a particle name if you want a labeled export and history row.
- Fill the required fields and select the correct units.
- Click Calculate Ratio to display the result above the form.
- Review the mass-to-charge ratio, reciprocal charge-to-mass ratio, and graph.
- Use the CSV or PDF buttons to export the current result or full session history.
Frequently Asked Questions
1. What does mass-to-charge ratio mean?
Mass-to-charge ratio shows how much mass belongs to each unit of electric charge. It is useful in beam physics, ion motion, spectroscopy, and mass analysis because particles with different ratios behave differently in fields.
2. Why can the result be negative?
A negative result usually appears when you enter a negative charge in the direct method. Mass stays positive, so the sign reflects charge polarity, not negative mass.
3. When should I use the magnetic field and velocity method?
Use that method when you know the particle path radius, magnetic field strength, and velocity. It fits circular motion problems in magnetic analyzers and beam experiments.
4. When is the accelerating voltage method helpful?
Use it when particles are first accelerated through a known voltage, then bent by a magnetic field. This is common in older mass spectrometry and ion beam setups.
5. What units should I use for best accuracy?
SI units are best because the formulas are naturally expressed in kilograms, coulombs, meters, tesla, meters per second, and volts. This calculator converts common alternatives automatically.
6. What is the difference between m/q and q/m?
They are reciprocals. Mass-to-charge ratio emphasizes mass per unit charge, while charge-to-mass ratio emphasizes charge per unit mass. Different textbooks and instruments prefer one form over the other.
7. Why does the graph use a logarithmic scale?
Particle ratios can differ by several orders of magnitude. A logarithmic scale makes very small and relatively larger values visible on the same chart without flattening the smaller values.
8. Does this calculator replace lab calibration?
No. It is a strong educational and planning tool, but real instruments still need calibration, uncertainty review, and method validation before you trust measured experimental results.