A drawing compass constrains the pencil to a fixed radius around its needle point. Two hinged legs and a setting screw hold the pencil at the selected radius as it traces a circle on the paper. Its calculator combines entered standard-uncertainty contributions and converts them to the corresponding full-size dimension for a reduced drawing.
Drawing Instrument Form Interactive Calculator
Watch a compass draw a circle with its needle fixed to the paper. Adjust radius, drawing scale and a clearly stated standard-uncertainty budget.
Equation Used
- Fixed 180 mm legs in the illustrative compass.
- Needle and pencil tips remain on the paper.
- Uncorrelated standard uncertainties with unit sensitivities.
- Drawing scale exact; known systematic effects corrected.
Uncorrelated standard-uncertainty inputs, unit sensitivities and exact reduction scale. No worst-case or confidence-level guarantee.
The needle stays planted while the pencil travels
The needle tip remains fixed at the circle center. The pencil tip stays on the paper at the selected radius. The hinge and both legs rotate together around the needle’s vertical axis; both model legs retain their fixed 180 mm length. The screw between the legs represents the radius-setting adjustment.
The view is an oblique projection, so a circle on the paper appears elliptical on screen. The blue dashed circle is the nominal path; the darker trace grows behind the pencil during each sweep. Changing radius alters the leg opening, not the length of the legs.
The separate uncertainty strip is magnified for reading. It is not a randomly distorted pencil path or a claim that the instrument moves through every possible error on each revolution.
Compare radius and an uncertainty budget
Set the drawing radius and reduction scale, then enter standard uncertainties for pivot location, flex, setting and operator effects in millimeters at the drawing. The calculator assumes these contributions are uncorrelated and already expressed as standard deviations with unit sensitivity to the reported radial quantity.
It does not convert arbitrary maximum errors into standard uncertainties. Known systematic effects should be corrected rather than treated as unexplained random motion.
Combined standard uncertainty and drawing scale
With uncorrelated standard-uncertainty contributions and unit sensitivities, u=√(up²+uf²+us²+uo²). For a drawing reduced at 1:S with exact scale, equivalent full-size standard uncertainty is Su.
The width of the illustrated interval from −u to +u is 2u. This is not a worst-case tolerance and does not by itself establish a 95% coverage interval. The u/0.05 comparison uses a stated 0.05 mm reference, not a universal drawing-quality standard.
Nominal circumference is 2Ï€R and equivalent full-size radius is SR. Uncertainty in the drawing scale itself is not included.
Example: a 100 mm radius at 1:8 scale
For pivot, flex, setting and operator standard uncertainties of 0.02, 0.30, 0.05 and 0.05 mm, combined u is approximately 0.309 mm. The −u to +u interval is approximately 0.618 mm wide, and equivalent full-size standard uncertainty is approximately 2.47 mm.
The nominal drawn circumference is 628.32 mm and equivalent full-size radius is 800 mm. Increasing radius changes those geometry results and the compass opening; it does not automatically change the uncertainty contributions the user supplied.
Uncertainty is not a wear or service-life prediction
Correlated contributions require covariance terms. Worst-case error bounds require a different interpretation from a root-sum-square combination of standard uncertainties. The page makes neither a confidence-level claim nor an instrument accuracy certification.
This generic compass has fixed 180 mm legs. Its geometry illustrates radius setting and circle drawing; instrument calibration and mechanical compliance require measurements of the actual tool.
Drawing-instrument questions
Why is the drawn circle an ellipse on screen?
The paper is shown in an oblique projection. The pencil remains at exactly the entered radius in the modeled paper plane.
Do uncertainty controls make the compass wobble?
No. They update the labeled uncertainty strip and results. A deterministic wobble would imply a time-dependent error model that has not been entered.
Is twice u a 95% band?
The displayed width is from −u to +u, which is 2u across. A coverage statement requires a probability model and an appropriate coverage factor.
Can I enter tolerance limits here?
Not directly as if they were standard deviations. Convert bounds using an appropriate distribution and account for correlations before using this simplified combination.
Construction and calculation references
STAEDTLER compass construction guide: hinged legs, needle point, lead and setting mechanism.
NIST Technical Note 1297, section 5: combined standard uncertainty. The simplified formula here assumes uncorrelated contributions and unit sensitivities.
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