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Showing 1–30 of 1709 reference entries

Mathematics & logicExamples and counterexamples

Learn what a claim covers, explain why it works, and recognise an allowed case that shows it needs changing.

MethodMathematics & logicCounting and zero

Count each object once, explain the final count, and distinguish quantity, position and identifying labels. Make zero’s role explicit.

DefinitionMathematics & logicNumber lines and order

Use number-line positions to compare whole numbers. Read the scale, recognise equality, and distinguish numerical distance from drawing size.

DefinitionMathematics & logicAddition and subtraction

Combine separate counts, remove a part, and find differences or missing parts. Connect objects, equations and number-line moves, then use tens and ones to regroup without changing value.

DefinitionMathematics & logicMultiplication and division

Count equal groups, distinguish sharing from making groups, and check with multiplication. Split calculations into parts; interpret zero and remainders in context.

DefinitionMathematics & logicFractions

Choose a whole, count equal fractional units, and connect sharing with division. Place fractions on the number line, including values beyond one, and explain what their numerator and denominator mean.

DefinitionMathematics & logic · Physics · MeasurementRatios and rates

Distinguish part-to-part ratios, fractions of a whole and rates with units. Scale quantities together, compare unit rates, and explain when a relationship is proportional. Check zero cases, starting amounts and whether a result fits its context.

DefinitionMathematics & logic · Physics · MeasurementQuantities and units

Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.

DefinitionMathematics & logic · Physics · MeasurementUnit conversions

Convert quantities with exact unit ratios, track cancellation through compound units, and apply the correct powers to area and volume. Distinguish temperature readings from differences, check dimensions and context, and retain measurement uncertainty when reporting.

MethodMathematics & logic · Physics · MeasurementEstimation and uncertainty

Distinguish exact model values, rounded approximations and estimates from measurements. Declare the rounding rule, preserve information through calculations and unit changes, and interpret resolution, precision, accuracy and the stated uncertainty type without turning a report’s digits into guaranteed bounds.

DefinitionMathematics & logicVariables and expressions

Use symbols to name numbers or quantities, describe their allowed values, and evaluate expressions by replacing every occurrence consistently. Preserve grouping, signs, fractions and units, and distinguish a calculated value from solving an equation or proving two rules equivalent.

DefinitionMathematics & logicEquality and equations

Read equality as a relationship, find the permitted values that make an equation true, and justify one-step solutions by reversible operations on both sides. Work exactly with negative numbers and fractions, recognize all-solution and no-solution cases, and check the original equation, units and context.

DefinitionMathematics & logic · PhysicsCoordinates and tables

Locate a point from an ordered pair, read named axes and their scales, and connect the same values in words, tables and plots. Keep signs, fractions and units exact, distinguish an axis point from a quadrant point, and separate selected observations from a stated rule and its domain before drawing connections.

DefinitionMathematics & logic · PhysicsSlope and straight lines

Read a straight line as a stated relationship, calculate its slope from consistent signed coordinate changes, and interpret its intersections with the axes. Keep horizontal, vertical and coincident-point cases distinct, attach units and domain conditions to context models, and use numerical scales rather than appearance alone to judge a line’s change.

DefinitionMathematics & logic · Physics · MeasurementReading graphs

Read a graph’s quantities, units, ticks and context before judging its visual impression. Calculate differences, reference-based percentages and interval rates from the represented values; distinguish legitimate zoom from distorted spacing; and keep samples, interpolation, missing information, uncertainty and causal explanations separate.

MethodPhysics · MeasurementObservables and measurement

Choose the physical quantity you want to investigate, specify the point, event or location involved, and explain how a reading relates to that quantity.

MethodPhysicsSystems and boundaries

Choose what belongs to an investigation, describe its condition at a stated time, and identify interactions with what lies outside its boundary.

MethodPhysicsModels and assumptions

Choose what a model represents, make its simplifications explicit, and check whether its predictions answer the physical question you actually asked.

MethodPhysicsHypotheses, laws and theories

Identify what a scientific statement does, examine its evidence and conditions, and avoid treating its name as a score for certainty.

MethodMathematics & logic · PhysicsApproximations

Build a useful estimate, compare a correction with a stated reference scale, and check what is lost when you leave out a term.

ApproximationMathematics & logic · PhysicsSymmetry and invariance

Specify a transformation, identify what stays unchanged, and distinguish symmetry of an object from invariance of a physical model.

Mathematical statementPhysicsConservation laws

Use a defined system and a named quantity to track transfers, distinguish changing parts from conserved totals, and check the conditions of energy and momentum balances.

ModelPhysicsEmergence and levels of description

Choose a descriptive level, connect collective quantities with component behavior, and check when a simpler physical description answers a specified question.

ModelMathematics & logic · PhysicsVectors

Describe displacement with fixed-axis components, combine compatible vectors, and use small exact examples to introduce span, independence, basis and real vector spaces.

DefinitionPhysics · Information · MeasurementScientific records

Build an inspectable physics record, test and revise a bounded cart model, preserve processing history, and plan findable data with appropriate sharing conditions.

MethodPhysicsPosition, velocity and acceleration

Describe a point's motion on a chosen straight axis, then connect signed changes, instantaneous rates and one exact set of position, velocity and acceleration graphs.

DefinitionPhysicsNewton’s laws and forces

Choose one body, identify the forces acting on it, and use their vector sum to distinguish acceleration, balanced motion and mutual interactions.

ModelPhysicsWork, energy and power

Connect force and displacement to changes in motion, follow a spring’s stored energy, and distinguish an energy transfer from its rate.

ModelPhysics · MeasurementSpeed of light in vacuum

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

DefinitionPhysics · MeasurementPlanck constant

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

Definition
DefinitionSource checked

Calibration

Measurement

Relate indications to standards, then infer measurement results.

Key knowledge

Calibration establishes, under stated conditions, a relation between standard values with uncertainty and instrument indications with uncertainty. That relation is then used to obtain a measurement result from an indication.

Conditions and scope

  • State the standards, uncertainties and calibration conditions.
  • Calibration is distinct from instrument adjustment or verification of a requirement.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. JCGM 200:2012 (VIM3), definition 2.39: calibrationJoint Committee for Guides in Metrology / BIPMReference guide · PDFbipm.orgRead source

Evidence and review

VIM3 2.39, both stages and notes 1–2; PDF inspected when the HTML page timed out.

2026-10-10 · Metrological definition only; no calibration certificate, instrument fitness or traceability automatically conferred.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–15 of 15 relationships

Scientific relationships · 15 / 15

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • Calibration establishes, under stated conditions, a relation between standard values with uncertainty and instrument indications with uncertainty. That relation is then used to obtain a measurement result from an indication.

    Documented calibration relations are elements in a metrological traceability chain; this definition does not certify a chain.

  2. Related to
    Relationship sources · 2

    Linked statements

    • Resolution is the smallest input change producing a perceptible indication change. Sensitivity is the ratio of indication change to input-quantity change; it can depend on operating value.

    Calibration relates indications to input quantity values; resolution and sensitivity describe conditional aspects of that response.

  3. Related to
    Relationship sources · 2

    Linked statements

    • For a linear time-invariant response in sinusoidal steady state, transfer function H(ω) = Y(ω)/X(ω) specifies output gain and phase. Step-response time instead needs a stated settling band around the final indication.

    PTB's dynamic amplifier calibration measures complex gain/phase over its stated linear range.

  4. Related to
    Relationship sources · 4

    Linked statements

    • Measurement error is measured value minus reference value. Bias estimates a systematic measurement error, and a correction compensates an estimated systematic effect by an addend, factor or other model. Uncertainty characterizes incomplete knowledge of the result and is distinct from a known error or an operational mistake.

    Calibration can supply a correction with uncertainty; an error relative to a reference is not an uncertainty width.

  5. Related to
    Relationship sources · 1

    Linked statements

    • A CCD records photo-generated charge in pixels over an exposure. A spectrometer distributes light by wavelength so that a detector can measure a spectrum. Distributing a fixed photon total over more spectral bins reduces counts per bin; exposure, collecting area and calibration affect the usable measurement.

    Detector signal requires a calibrated relation to a measurand.

  6. Related to
    Relationship sources · 1

    Linked statements

    • Photometric counts need a calibrated band response and zero point before they represent an astronomical flux or magnitude. For positive flux F with small standard uncertainty u(F), first-order propagation through m=−2.5log₁₀F+C gives u(m)≈[2.5/ln10]u(F)/F. Calibration and extinction uncertainties remain separate contributions.

    Zero points and response corrections require calibration.

  7. Related to
    Relationship sources · 2

    Linked statements

    • In a Newtonian isolated two-body Keplerian model, the host star's line-of-sight orbital velocity has semi-amplitude K=(2πG/P)^(1/3) Mp sin i/[(Mstar+Mp)^(2/3)√(1−e²)]. The mass function follows by cubing: PK³(1−e²)^(3/2)/(2πG)=Mp³ sin³i/(Mstar+Mp)². Without inclination and stellar-mass constraints this does not give a unique true companion mass. For Mp much smaller than Mstar it commonly constrains Mp sin i.

    Spectral velocity estimates depend on calibrated instrumental response.

  8. Related to
    Relationship sources · 2

    Linked statements

    • A genetic perturbation tests a causal prediction when the intended change and relevant phenotype are measured against appropriate controls. Agreement across independent perturbations or clones and restoration by a suitable resistant allele can strengthen gene-function attribution. DNA alteration, transcript level, protein detection and phenotype are different readouts; none automatically certifies all the others.

    Readouts need method-specific response and uncertainty checks.

  9. Related to
    Relationship sources · 1

    Linked statements

    • In a suitable transmitted-light grain–medium boundary test, increasing the objective-to-specimen separation moves the Becke bright line into the material of higher refractive index. Relief decreases near index matching. Comparison with calibrated immersion media can constrain a grain's refractive index at a specified wavelength and temperature.

    Immersion standards and environmental effects require calibration.

  10. Related to
    Relationship sources · 1

    Linked statements

    • Unsaturated water content θ and conductivity K depend on pressure head ψ and the medium's pore structure. A specified retention branch gives moisture capacity C(ψ)=dθ/dψ. Wetting and drying can follow different branches, so one pressure head may correspond to different water contents. Conductivity and retention are required constitutive data rather than consequences of Darcy's law alone.

    Constitutive curves depend on a documented measurement process.

  11. Related to
    Relationship sources · 2

    Linked statements

    • Passive sensors receive externally supplied or naturally emitted radiation; active radar/lidar supplies illumination and measures its return. A spectral band records a wavelength-weighted signal from a spatial footprint, not direct composition at a mathematical point. Surface reflection/emission, atmospheric transmission/scattering and observation geometry jointly affect the measured signal.

    A measured sensor signal requires a calibration model.

  12. Related to
    Relationship sources · 3

    Linked statements

    • A sensor is the element directly affected by the phenomenon, body or substance carrying the quantity to be measured. A measuring transducer provides an output quantity with a specified relation to an input quantity. A detector indicates the presence of a phenomenon, body or substance when a threshold is exceeded. The same physical component may fulfil more than one role in an assembled system.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  13. Related to
    Relationship sources · 2

    Linked statements

    • An indication is a quantity value provided by a measuring instrument or system. A measurement result is the set of quantity values attributed to the measurand together with relevant available information; ordinarily it includes a measured value and its uncertainty. The indicated quantity may differ in kind from the inferred measurand, so a reading can require conversion through the measurement model.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  14. Uses definition
    Relationship sources · 2

    Linked statements

    • Adjustment comprises operations that make a measuring system provide prescribed indications for given values of the measured quantity. Zero adjustment is the adjustment producing a null indication for a zero value. Calibration is a prerequisite for adjustment and is usually required again afterwards; adjustment must not be called calibration. Setting zero alone does not establish correct gain, response across the interval or zero uncertainty.

    This relation concerns the stated adjustment, calibration and zero adjustment claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  15. Related to
    Relationship sources · 3

    Linked statements

    • An indication interval is bounded by the extreme possible indications. Its span is the absolute difference between those extremes. A measuring interval is the set of quantity values measurable with a specified instrumental uncertainty under defined conditions. A ±10V indication interval has20V span, but that interval alone does not establish a20V measuring capability. The lower limit of a measuring interval need not equal a detection limit.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

Entry detailsPermanent link to this entry ↗
Record identity
measurement-calibration
Revision
university-reference.1
Structured reference record
University reference · University core expansion