Resolution is not mass accuracy

Applied measurement skills

Describe what improved, and what did not

Prerequisite: You can read a spectrum's m/z axis. Allow about 20 minutes with the model. You will calculate a peak width, a signed mass error and a repeatability summary, then decide what evidence is still missing.

State resolving power with its reference m/z and peak-width criterion
Distinguish one measured mass error from an estimate of systematic bias
Explain why an overlapping signal can move a reported centroid
Use mass agreement to test a candidate without claiming it uniquely identifies a compound

Predict: narrow but shifted

An isolated synthetic peak has reference m/z 500.0000, a component center at 500.0025 and FWHM 0.0100 in m/z. You make it four times narrower without changing its center. Has its mass error improved?

Reveal the answer

No. The width decreases to 0.0025, so R_FWHM increases from 50,000 to 200,000 at m/z 500. The center remains 0.0025 high, corresponding to +5 ppm. Narrowing and moving a peak are separate changes in this model.

A real processing algorithm can change a reported centroid when overlap or signal quality changes. That is a reason to inspect how a value was produced, not a reason to equate resolution with accuracy.

Four quantities, four questions

Keep these questions separate
Quantity	Question it answers	Evidence needed
Peak width / resolving power	How narrow is the signal at a stated criterion?	A suitable peak, reference m/z and width definition
Signed mass error	How far is this measured value from the reference?	Correct ion reference and a stated measurement
Bias estimate	Does a measurement process tend to read high or low?	Repeated suitable reference measurements and their conditions
Precision under stated conditions	How much do repeated values vary?	Replicates, conditions and a statistic such as standard deviation

Mass accuracy describes agreement with a reference, while a numerical mass error reports one comparison. Repeated measurements help distinguish a persistent offset from scatter. A small spread can coexist with a substantial offset. NIST's bias discussion and variability discussion provide the measurement-process context.

Calculate width with a declared convention

This site uses R_FWHM = x / w, where x is the numerical m/z coordinate at which the width is specified and w is the full width at half maximum on the same m/z scale. R is dimensionless. “Full width” means the distance between the two half-height crossings of a suitable peak, not the distance from its center to one crossing.

At x = 500 and R_FWHM = 50,000, w = 500/50,000 = 0.0100 in m/z. At x = 1000 with the same R, w = 0.0200. Do not transfer a resolving-power specification between m/z values without knowing the analyzer's behavior and acquisition conditions. The IUPAC peak-width definition requires a stated height criterion; a 10% valley criterion is a different convention.

Worked example: test a tempting separation rule

Two equal Gaussian components sit at 500.0000 and 500.0100. Each has FWHM 0.0100. Their centers are one FWHM apart. Does this mean they are baseline separated?

At their midpoint, each component is one half-width from its own center, so each contributes half its individual maximum. Their sum at the midpoint is therefore 1.0 when each isolated component height is 1. The combined signal between them is substantial. “Separation equals FWHM” is not a baseline-separation rule.

The precise valley depends on the entire summed shape. Unequal peak heights and noise further complicate visual distinguishability. A useful report states the criterion instead of declaring “resolved” from a single ratio.

Calculate a signed mass error

For a measured coordinate x_meas and reference x_ref,

error (ppm) = 10⁶ × (x_meas − x_ref) / x_ref

The denominator is the reference. A positive result means measured high; a negative result means measured low. Parts per million express a relative difference. Keep the sign during diagnosis even if a matching rule ultimately uses the magnitude.

Worked example: +5 ppm is not +0.005 everywhere

At reference 500.0000, a measured 500.0025 has error 10⁶ × 0.0025/500 = +5 ppm
At reference 200.0000, +5 ppm corresponds to +0.0010 in m/z
At reference 1000.0000, +5 ppm corresponds to +0.0050 in m/z

An illustrative ±5 ppm window around reference 500.0000 spans 499.9975 to 500.0025. That arithmetic is not a recommended acceptance limit. Choose tolerances from the validated method, instrument performance and purpose of the comparison.

Use the correct reference ion, charge state, adduct and isotope. Comparing a measured [M+Na]⁺ value with a calculated [M+H]⁺ value does not diagnose calibration: it tests the wrong assignment. Review ion families and isotope spacing if those possibilities are not yet clear.

Manipulate one assumption at a time

Use the synthetic model below in three passes. First keep offset at +5 ppm and change resolving power from 50,000 to 200,000. Then hold width fixed and set offset to zero. Finally reduce the second peak's height to 0.1 and add a little synthetic noise. For each pass, name the changed quantity before looking at the plot.

What should those three experiments teach?

Higher R reduces width. It does not remove the specified component-center offset
Zero offset aligns the known model centers with the references. It does not narrow either component
A small neighboring component can become harder to see beside a larger one. The model's known centers remain available because we constructed them; a real analyst does not automatically know the components of an unresolved peak

The noise control is repeatable synthetic variation, not a detector simulation or a validated signal-to-noise calculation. The plot rescales; compare the numerical widths, not only how wide a peak looks on your screen.

A reported center can depend on overlap

The explorer displays the true component centers used to construct its Gaussian curves. A real processing workflow must estimate peak positions from data. The maximum of a summed peak, its intensity-weighted centroid and the center of a fitted component need not be the same number.

To isolate the idea, suppose two ideal sticks are at 500.0000 and 500.0100 with weights 1.0 and 0.2. If a hypothetical algorithm collapses them into their intensity-weighted mean, it returns:

(1 × 500.0000 + 0.2 × 500.0100) / 1.2 = 500.0016667

Relative to the first component, that is about +3.33 ppm, even though neither input position was shifted. This arithmetic illustrates interference; it is not a universal description of centroiding software. Actual algorithms, peak shapes, thresholds and fitting choices differ.

Check: should you recalibrate from that +3.33 ppm alone?

No. First test whether the measurement is an appropriate isolated reference, whether an interfering component or processing choice changed the reported position, and whether independent references show a consistent error. A calibration change based on an interference-biased peak can move otherwise correct assignments.

Repeatability needs repeated measurements

Consider five synthetic measurements of the same reference ion at m/z 500.0000, collected under the same stated conditions: 500.0020, 500.0025, 500.0030, 500.0025, 500.0025.

Worked example: a repeatable offset

The mean is 500.0025, corresponding to a mean error of +5 ppm
The sample standard deviation, using n − 1 = 4 in the denominator, is approximately 0.000354 in m/z, or 0.707 ppm relative to 500
The values are tightly grouped around a value above the reference. Good short-term repeatability has not removed the offset

Five artificial replicates demonstrate arithmetic, not a complete uncertainty budget. A real study would consider reference uncertainty, independence, signal range, matrix, acquisition mode and changes across time. State what conditions were held constant and which were varied.

Peak width describes a distribution within a spectrum. Replicate standard deviation describes a distribution of measured values across measurements. Both have “spread” in their everyday meaning, but they are not interchangeable statistics.

Apply: choose a useful next check

A sample feature matches a candidate within 1 ppm. Your blank contains a nearby feature, the sample peak is asymmetric, and no authentic standard has been measured. Write a defensible conclusion and one next comparison.

Compare your answer with an evidence-first response

“The measured feature is mass-consistent with the proposed ion within the stated tolerance; identity is not established.” Inspect the blank and sample chromatographic context and profile shape, check the ion/adduct/isotope assignment, and test independent evidence such as suitable MS/MS or an authentic reference under relevant conditions.

A small error narrows some possibilities. It does not make an asymmetric, possibly contaminated feature chemically unique. Multiple formulas can lie in one mass window, and isomers can share a formula and exact mass.

Check your understanding

A peak at reference m/z 400 has FWHM 0.0080. Calculate R_FWHM
The reference is 400.0000 and measured value 399.9988. Calculate the signed error
Would ten identical measurements at 399.9988 establish agreement with the reference?
A manufacturer quotes a resolving-power value without its reference m/z or criterion. What should you ask for?

Worked answers and why they matter

400/0.0080 = 50,000 at m/z 400 under the FWHM criterion
10⁶ × (−0.0012)/400 = −3 ppm; the measurement is low
No. They would show no displayed scatter in this example but retain a −3 ppm difference. Rounding can also hide variation
Ask for the reference m/z, width or valley criterion, acquisition conditions and how the value was measured. Comparisons require compatible definitions

A better measurement statement

Instead of “the peak looks good,” record the ion assignment and reference, measured position and signed error, width criterion and reference m/z, relevant replicate performance, and any overlap or processing caveats. These observations help you decide whether a problem concerns calibration, transmission, interference, processing or the proposed chemistry.

For example: “Synthetic [specified ion] reference m/z 500.0000; measured component center 500.0025 (+5 ppm); FWHM 0.0100, giving R_FWHM = 50,000 at m/z 500. No identity claim follows from this example.”

Primary references

IUPAC, resolution: peak width definition: why the peak-height criterion belongs with the number
IUPAC, accurate mass: measured accurate mass versus calculated exact mass
NIST, Bias and Accuracy: reference agreement and systematic offset
NIST, Variability: repeated measurements and their conditions

All spectra, peak lists, tolerances and replicate datasets here are original synthetic teaching examples. They are not instrument-performance or method-validation results.

Take the distinction to the instrument

Continue with Calibration vs tuning to distinguish mass-axis correction, ion-optics optimization and independent verification. Return to the standalone lab for a guided comparison without the full lesson.