Understand the relationship
The reasoning behind the result
A reference establishes physical length per image pixel
sx = Lx/Px; sy = Ly/Py
A known specimen-plane reference length L spanning P image pixels gives scale s = L/P. The reference must belong to the same acquisition settings and image state as the measurements. An axis-aligned reference calibrates that axis; one horizontal span does not establish an unknown vertical scale.
Same-scale mode explicitly assumes equal horizontal and vertical specimen scales. Separate-axis mode preserves anisotropic calibration. These quantities describe pixel spacing, not optical resolving power, boundary localization uncertainty or a universal measurement precision.
Nominal sensor geometry is an estimate that can be checked
s = pnative b/(Mo Mr)
pnative is native sensor pitch, b is the number of native pixels combined along that axis, Mo is effective objective magnification and Mr is camera relay magnification. Dividing the binned sensor pitch by the optical lateral magnification maps it back to the specimen plane.
The model assumes a simple camera path with known factors and no unaccounted scaling. It does not include an eyepiece's visual magnification. Nominal pitch and optical factors are useful for planning but do not replace a stage-micrometer calibration of the actual final image.
Resampling changes the pixel scale
sfinal,x = sx/Rx; sfinal,y = sy/Ry
Rx is the ratio of output pixel count to input pixel count along the horizontal axis for a resize of the same field; Ry is the corresponding vertical ratio. Doubling pixel count halves physical length per pixel. Halving pixel count doubles it. Horizontal and vertical ratios can differ.
Cropping removes image extent without changing pixel spacing. The optional final image dimensions therefore describe the actual final crop or frame. Field width and height are final pixel counts times the corresponding final scales. Resampling adds no optical information, and metadata copied from another image can be stale.
Calibrate vector components before taking their length
ΔX = Δx sx; ΔY = Δy sy; L = √(ΔX² + ΔY²)
Measured pixel displacements Δx and Δy may be signed. Their physical components must each use the correct axis scale before the two-dimensional Euclidean length is formed. Multiplying a raw diagonal pixel length by one arbitrary scale is incorrect when scales differ.
Target-length mode instead reports separate horizontal and vertical pixel spans for the same physical length. Those are axis-aligned alternatives, not the components of one diagonal. The pixel area sx sy is the area represented by a single calibrated pixel cell; it does not identify which cells belong to a specimen.
Follow the numbers
Preserve a physical diagonal through a nonuniform resize
- A 100 µm standard spanning 500 pixels gives 0.2 µm per pixel on both axes under the stated isotropic assumption.
- A 300-pixel horizontal and 400-pixel vertical displacement becomes 60 µm by 80 µm, with length √(60² + 80²) = 100 µm.
- After width is halved and height doubled, scales become 0.2/0.5 = 0.4 µm/pixel and 0.2/2 = 0.1 µm/pixel.
- The same displacement is now 150 by 800 pixels: 150 × 0.4 = 60 µm and 800 × 0.1 = 80 µm, still 100 µm long.
Per-axis calibration preserves physical dimensions through the declared resize; an unchanged single pixel scale would not.
Quick guide
How to use this calculator
- Choose a measured standard, independently known scale or nominal sensor model. A calibration reference must use the same optical and image settings as the measurements.
- Keep horizontal and vertical scales separate if pixels are not isotropic in specimen space. Sensor pitch always uses micrometres; other physical inputs use the chosen unit.
- Declare only resizing that happened after the entered calibration. Binning already incorporated in a measured or known scale must not be applied twice.
- Optionally enter final image dimensions and named displacements or target lengths. Review per-axis components before interpreting a diagonal length.
Calculation method
Calculation and interpretation
Keep each image axis calibrated through measurement, binning and resizing.
sx = Lx/Px; sy = Ly/Py; snominal = native sensor pitch × binning / (objective × relay); sfinal = sbefore / resize ratio; L = hypot(Δx sx, Δy sy); Apx = sx sy.
Worked example
Preserve a physical diagonal through a nonuniform resize
Per-axis calibration preserves physical dimensions through the declared resize; an unchanged single pixel scale would not.
sx = Lx/Px; sy = Ly/Py; snominal = native sensor pitch × binning / (objective × relay); sfinal = sbefore / resize ratio; L = hypot(Δx sx, Δy sy); Apx = sx sy.
Supported inputs
Precision and limits
Calibration must match the image
No file metadata is read or edited. Match objective, relay, binning, zoom, acquisition dimensions and image transformations yourself. Distortion, shear, perspective and nonlinear warping require a richer calibration than two orthogonal scales.
Geometric conversion only
No segmentation, diagnosis, uncertainty estimate or resolution guarantee is inferred. Positive dimension, scale and magnification inputs support 10⁻¹² through 10¹² in their selected units. Signed displacement components may be exactly zero; nonzero components must have an absolute magnitude from 10⁻¹² through 10¹². These are numerical bounds, not equipment specifications or accuracy claims.
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