Time-of-Flight Mass Spectrometry Calculator

What is Time-of-Flight Mass Spectrometry?

Time-of-Flight (TOF) mass spectrometry identifies molecules by measuring how long their ions take to fly through a vacuum tube after being accelerated by a known electric field. Heavier ions move slower than lighter ones given the same kinetic energy, so the flight time directly reveals the mass-to-charge ratio (m/z). TOF instruments are used in drug discovery, proteomics, forensics, and airport security screening.

Mathematical Foundation

TOF Flight Time

t = L \sqrt{\frac{m}{2qV}}

t

= Flight time through the drift tube (seconds).

L

= Length of the field-free drift tube (meters).

m

= Mass of the ion (kg).

q

= Charge of the ion (Coulombs).

V

= Accelerating voltage applied to the ion source (Volts).

Laws & Principles

Equal Kinetic Energy Principle: All ions leaving the accelerating region receive the same kinetic energy (KE = qV). Since KE = (1/2)mv^2, lighter ions travel faster than heavier ones through the drift tube.
Mass Resolution: Resolution in TOF depends on the precision of the flight time measurement. Modern reflectron-TOF instruments achieve resolving powers of 20,000-60,000, distinguishing ions that differ by less than 0.001 Da.
Charge State: Multiply charged ions (z = 2, 3, etc.) appear at apparent m/z values lower than their true mass. A 1000 Da protein with z = 2 appears at m/z = 500.

Step-by-Step Example Walkthrough

" A singly charged ion (z=1, q = 1.602e-19 C) is accelerated through 20,000 V and travels a 2.0 m drift tube. It arrives in 45.2 microseconds. What is the ion mass? "

1. Rearrange the formula: m = 2qV * (t/L)^2.
2. Calculate t/L: 45.2e-6 / 2.0 = 2.26e-5 s/m.
3. Square the ratio: (2.26e-5)^2 = 5.108e-10.
4. Multiply: 2 * 1.602e-19 * 20000 * 5.108e-10 = 3.27e-24 kg.
5. Convert to Daltons: 3.27e-24 / 1.661e-27 = 1968 Da.

Final Result: The ion has a mass of approximately 1968 Daltons, consistent with a small peptide or large drug molecule.

Analyte Class	Typical Mass Range (Da)	Ionization Method
Small Organic Molecules	50 - 1,000	EI, ESI, APCI
Peptides	500 - 5,000	MALDI, ESI
Intact Proteins	5,000 - 200,000	MALDI, Native ESI
Synthetic Polymers	1,000 - 100,000	MALDI

Analyte Class

Typical Mass Range (Da)

Ionization Method

Small Organic Molecules

50 - 1,000

EI, ESI, APCI

Peptides

500 - 5,000

MALDI, ESI

Intact Proteins

5,000 - 200,000

MALDI, Native ESI

Synthetic Polymers

1,000 - 100,000

MALDI

Instrument Configurations

Linear TOF

Ions fly in a straight line from the source to the detector. Simple design with high sensitivity, but lower mass resolution (~5,000). Best for high-mass analytes like intact proteins where resolution is less critical than detection limits.

Reflectron TOF

An electrostatic mirror at the end of the drift tube reverses the ion direction. Faster ions penetrate deeper into the reflectron and travel a longer path, correcting for initial kinetic energy spread. This doubles the effective path length and increases resolution to 20,000-60,000.

Calculation Best Practices (Pro Tips)

Do This

✓Convert mass to kilograms before calculating. The formula requires SI units. 1 Dalton (atomic mass unit) = 1.661 x 10^-27 kg. Forgetting this conversion produces flight times that are off by many orders of magnitude.
✓Account for ion charge state. A doubly charged ion (z=2) has q = 2 * 1.602e-19 C, giving it twice the kinetic energy of a singly charged ion at the same voltage. It flies faster and appears at half the expected m/z value.

Avoid This

✗Do not ignore isotope peaks. Most elements have natural isotopes. Carbon-13 is 1.1% of all carbon atoms, so a molecule with 100 carbons will show a significant M+1 peak. This is expected behavior, not instrument error.
✗Do not assume linear mass-time scaling. Because flight time scales with the square root of mass, a molecule twice as heavy does not take twice as long. It takes only 1.414 times as long.

Frequently Asked Questions

What is the difference between MALDI-TOF and ESI-TOF?

MALDI (Matrix-Assisted Laser Desorption/Ionization) uses a pulsed laser to vaporize a dried sample mixed with a UV-absorbing matrix. It produces mostly singly charged ions and works well for large biomolecules. ESI (Electrospray Ionization) sprays a liquid sample through a charged capillary, producing multiply charged ions. ESI is better for coupling with liquid chromatography (LC-MS).

Why does the drift tube need to be under vacuum?

Ions must travel the entire drift tube length without colliding with gas molecules. At atmospheric pressure, the mean free path of a gas molecule is only about 68 nanometers. Under high vacuum (10^-6 to 10^-8 Torr), the mean free path extends to meters, allowing ions to fly unimpeded from source to detector.

What does a reflectron do?

A reflectron is a series of ring electrodes that create an electrostatic mirror. Ions of the same m/z but slightly different kinetic energies penetrate the reflectron to different depths. The faster (higher energy) ions travel a longer path and arrive at the detector at the same time as the slower ones. This energy focusing dramatically improves mass resolution.

How accurate are TOF mass measurements?

Modern reflectron-TOF instruments routinely achieve mass accuracy of 1-5 parts per million (ppm). For a 500 Da molecule, that means the measured mass is accurate to within 0.0005-0.0025 Da. This precision is sufficient to determine the molecular formula of unknown compounds by matching the exact mass against chemical databases.