Start with the quantity
Which variable actually answers your question?
IB Mathematics · Experiments and measurement data
Choose measurement tools that match the mathematical question.
From rulers and thermometers to data loggers, video analysis, CO₂ sensors and Python - with data types, mathematics, topic examples and limitations.
Choose equipment purposefully
Measurement tools for IB Mathematics experiments
Measuring equipment does not automatically make an IA strong. The measured quantity must match the research question, the data must be reproducible, and you must explain resolution, accuracy, uncertainty and limitations. This guide connects common devices with mathematical methods and possible topic directions.
Separate resolution and accuracy
A display in 0.1 increments does not automatically prove ±0.1 accuracy.
Calibrate and pilot
Run a short pilot before collecting the full series.
Repeat
Multiple trials reveal variation, outliers and uncertainty.
Preserve raw data
Keep original files, settings and timestamps traceable.
Safety and privacy
Heat, electricity, sport, personal or health data require additional safeguards.
From device to research question
Plan the variable, sampling interval and analysis together.
- Question: Which relationship or model will be investigated?
- Measurement plan: Which values, intervals, controls and repetitions are needed?
- Mathematics: Which functions, regressions, distributions or optimisations answer the question?
- Reflection: How do measurement error and model assumptions affect the result?
Basic measurements
Basic measurements
Ruler, tape measure, calliper and protractor
What you can do with it
Use these tools to measure length, diameter, thickness, angle and geometric distance. A calliper is valuable when millimetres or tenths of a millimetre matter; a protractor supports projectile, light, solar and slope experiments.
- Typical data
- Length, angle, area, volume, ratio, measurement error
- Mathematics
- Geometry · Trigonometry · Regression · uncertainty
Example topics
- Paper-aeroplane trajectory at different launch angles
- Volume of irregular or solids-of-revolution objects
- Solar-cell output as a function of incidence angle
Practical and safety notes
Search related topics →Record resolution and measurement method. Repeat readings and keep the same reference points.
Scale and precision balance
What you can do with it
A kitchen scale is sufficient for gram-level readings; a precision balance is better for evaporation, filter residue, electrodes or small material samples. Mass time series can be analysed with linear, exponential or piecewise models.
- Typical data
- Mass, mass change, density, loss rate
- Mathematics
- Regression · calculus · statistics · uncertainty
Example topics
- Evaporation rate of different liquids
- Density of wood, plastics or solutions
- Mass gained by filters or water absorbed by materials
Practical and safety notes
Search related topics →Use the same container, tare before each run, and protect the balance from draughts and splashes.
Measuring cylinder, pipette and lab vessels
What you can do with it
Measuring cylinders provide reproducible volumes; pipettes are useful for small, accurately dispensed quantities. They support concentration series, density measurements and controlled flow or mixing experiments.
- Typical data
- Volume, concentration, flow, density
- Mathematics
- Proportionality · regression · differential equations · uncertainty
Example topics
- Drainage time for different outlet areas
- Density of water–ethanol mixtures
- Effect of sugar concentration on flow rate
Practical and safety notes
Search related topics →Read the meniscus at eye level. Chemicals and hot liquids require appropriate school-lab supervision and protection.
Stopwatch, timer and light gate
What you can do with it
Time measurement is central to motion, reaction, cooling, oscillation, flow and decay. A phone timer is enough for slow processes; video or a light gate is much better for short intervals.
- Typical data
- Time, period, travel time, reaction time
- Mathematics
- Kinematics · regression · statistics · periodicity
Example topics
- Pendulum period as a function of length
- Flow or drainage times
- Learning curves and reaction-time distributions
Practical and safety notes
Search related topics →Separate device resolution from human reaction delay. Manual timing requires many repetitions.
Temperature, light and environment
Temperature, light and environment
Contact thermometer and temperature data logger
What you can do with it
A contact probe measures the temperature of an object, liquid or the air at the sensor. Data loggers record at fixed intervals, making them ideal for cooling, conduction, insulation and daily cycles.
- Typical data
- Temperature, temperature difference, rate of change, time constant
- Mathematics
- Exponentials · differential equations · regression · residual analysis
Example topics
- Newton cooling of drinks
- Insulation performance of cup materials
- Temperature profiles in rooms or soil samples
Practical and safety notes
Search related topics →Check immersion depth, response time and calibration. A liquid probe should not touch the vessel wall.
IR thermometer and thermal camera
What you can do with it
An IR thermometer measures surface temperature at a point without contact. A thermal camera produces spatial temperature fields for profiles, area means, cooling curves and image analysis.
- Typical data
- Surface temperature, temperature field, hotspots, spatial gradient
- Mathematics
- Regression · area analysis · interpolation · calculus
Example topics
- Heat distribution around bearings after motion
- Cooling of different cup surfaces
- Comparison of insulation materials or windows
Practical and safety notes
Search related topics →Emissivity, reflections and distance affect readings. Do not infer medical diagnoses from skin images; anonymise any personal imagery.
Humidity, material-moisture and weather instruments
What you can do with it
Hygrometers, moisture sensors, anemometers, rain gauges and pressure sensors create environmental time series suitable for multiple regression, seasonal patterns and controlled comparisons.
- Typical data
- Relative humidity, wind, precipitation, pressure, material moisture
- Mathematics
- Time series · multiple regression · statistics · periodicity
Example topics
- Humidity and evaporation rate
- Local wind and heat loss
- Material moisture and Wi-Fi attenuation
Practical and safety notes
Search related topics →Do not expose sensors to sun or rain unless rated for it. Document a constant location and measurement height.
Lux meter, light sensor and solar sensor
What you can do with it
Lux meters measure illuminance; suitable solar sensors or multimeters can measure electrical output. They support inverse-distance models, angle of incidence, shading and daily cycles.
- Typical data
- Lux, irradiance, voltage, power, angle
- Mathematics
- Trigonometry · power models · regression · optimisation
Example topics
- Solar-cell output at different angles
- Light intensity and plant response
- Illuminance distribution in classrooms
Practical and safety notes
Search related topics →Lux is weighted to human vision and is not identical to radiant power. Control sensor orientation and ambient light.
Electrical, mechanical and acoustic
Electrical, mechanical and acoustic
Multimeter and electrical meters
What you can do with it
A multimeter measures voltage, current and resistance. With a defined load it can support battery-discharge, internal-resistance, solar-cell and sensor-response investigations.
- Typical data
- Voltage, current, resistance, power, energy
- Mathematics
- Functions · regression · integration · optimisation
Example topics
- Battery discharge curves
- Internal resistance versus temperature
- Solar-cell power versus light angle and distance
Practical and safety notes
Search related topics →Use only safe low-voltage circuits. Connect current ranges correctly; mains electricity is not suitable for a student experiment.
Force sensor, spring balance and torque sensor
What you can do with it
These devices measure tension, compression, spring force and sometimes torque. Typical uses include Hooke’s law, friction, failure load, levers and optimisation of mechanical models.
- Typical data
- Force, extension, friction, breaking load, torque
- Mathematics
- Linear regression · optimisation · mechanics · uncertainty
Example topics
- Spring constant and working range
- Friction coefficient of different materials
- Bending or breaking load of standard samples
Practical and safety notes
Search related topics →Do not exceed rated loads. Fracture tests need eye protection, containment and competent supervision.
Microphone, sound-level meter and audio analysis
What you can do with it
Microphones provide waveforms and spectra; sound-level meters report levels in decibels. Software supports Fourier analysis, resonance, attenuation and reverberation time.
- Typical data
- Frequency, amplitude, decibels, spectrum, reverberation time
- Mathematics
- Sinusoids · Fourier analysis · logarithmic models · regression
Example topics
- Resonance frequency of tubes
- Sound attenuation by materials
- Overtones of musical instruments
Practical and safety notes
Search related topics →Keep microphone position and gain fixed. Protect hearing and avoid unnecessary sound levels.
Phone, camera and tracking
Phone, camera and tracking
Camera and smartphone for photo/video analysis
What you can do with it
Video makes position, angle and time measurable frame by frame. Photographs support area fractions, symmetry, fractals, perspective and spatial interpolation. Include a calibration length in the image.
- Typical data
- Pixel coordinates, distance, velocity, angle, area
- Mathematics
- Kinematics · regression · geometry · image analysis
Example topics
- Trajectory of a ball or paper aeroplane
- Rotational motion in sport
- Bubble fraction, leaf area or filter area from images
Practical and safety notes
Search related topics →Fix the camera, control perspective and record the frame rate. Obtain consent before recording people.
Phone sensors: accelerometer, gyroscope and magnetometer
What you can do with it
Many phones record acceleration, angular velocity and magnetic field. This supports oscillation, rotation, travel, inclination and relative field measurements.
- Typical data
- Acceleration, angular velocity, orientation, magnetic field
- Mathematics
- Vectors · periodicity · integration · power models
Example topics
- Damping of a pendulum or vehicle
- Magnetic field strength versus distance
- Acceleration profiles during motion
Practical and safety notes
Search related topics →Document sensor axes and sampling rate, subtract background values and secure the phone safely.
GPS device and fitness tracker
What you can do with it
GPS and trackers provide position, distance, speed, elevation, time and sometimes heart rate. They support real motion datasets, routes, elevation profiles and statistical comparisons.
- Typical data
- Coordinates, distance, speed, elevation, time series
- Mathematics
- Vectors · geometry · regression · statistics
Example topics
- Cycling speed and gradient
- Route optimisation to school
- Pacing and performance variation in running
Practical and safety notes
Search related topics →GPS errors increase indoors and near tall buildings. Protect privacy and do not publish precise home or health data.
Non-invasive physiology sensors
What you can do with it
Heart-rate, reaction-time or simple breathing sensors can record temporal patterns and differences between conditions. They are for low-risk observation, not diagnosis or self-intervention.
- Typical data
- Heart rate, reaction time, breathing period, recovery curve
- Mathematics
- Statistics · regression · exponentials · hypothesis tests
Example topics
- Recovery after standardised light activity
- Reaction time under different conditions
- Periodic modelling of breathing
Practical and safety notes
Search related topics →Consent, anonymisation and school rules are essential. Do not conduct risky exertion, medication trials or diagnoses.
Sensors and school laboratory
Sensors and school laboratory
pH, conductivity and salinity meter
What you can do with it
These sensors quantify properties of solutions, enabling calibration curves, concentration models, temperature corrections and time-dependent mixing or reaction studies.
- Typical data
- pH, conductivity, salinity, concentration
- Mathematics
- Logarithms · regression · calibration · uncertainty
Example topics
- Conductivity of rainwater samples
- Salinity and sound or freezing properties
- pH during dilution or neutralisation
Practical and safety notes
Search related topics →Use only safe substances and school-appropriate concentrations. Rinse and calibrate probes and document temperature dependence.
CO₂ sensor and indoor-air data logger
What you can do with it
A suitable NDIR CO₂ sensor records concentration, often with temperature and humidity, over time. It supports rise, decay and air-exchange models.
- Typical data
- CO₂ concentration, rate of change, time constant, air exchange
- Mathematics
- Exponentials · differential equations · multiple regression · time series
Example topics
- CO₂ decay after room occupancy
- Window opening and ventilation effectiveness
- Light intensity and net plant CO₂ exchange
Practical and safety notes
Search related topics →Do not deliberately enrich occupied rooms with CO₂ or seal people inside. Record warm-up time, drift and sensor position.
Specialist school-lab equipment
What you can do with it
Light gates, ultrasonic sensors, force plates, spectrometers, magnetic stirrers or precise data loggers can support demanding questions. A device is useful only when its measurement matches the research question and its operation is understood.
- Typical data
- Device-specific data at high temporal or spatial resolution
- Mathematics
- depending on experiment: calculus · statistics · differential equations · spectral analysis
Example topics
- Speed of sound in water
- Induced voltage from a moving magnet
- Controlled thermal or flow experiments
Practical and safety notes
Search related topics →Agree access with the teacher. Test limits, calibration, safety rules and data export before the main data collection.
Modelling, software and data
Modelling, software and data
Physical model, material samples and 3D printer
What you can do with it
Models provide controlled geometry, interchangeable parameters and repeatable trials. A 3D printer can produce channels, blades, vessels, bridges, tessellations or sensor mounts.
- Typical data
- Geometry, dimensions, load, flow, optimisation parameters
- Mathematics
- Geometry · optimisation · scaling · simulation
Example topics
- Channel cross-section and discharge
- Bridge curvature and material use
- Water-wheel blade angle
Practical and safety notes
Search related topics →Document print settings and dimensional error. Physical models simplify reality; those assumptions belong in the reflection.
Computer, spreadsheet, CAS, GeoGebra, Desmos and Python
What you can do with it
These tools store data, run regressions, create graphs, calculate residuals, simulate random processes and solve equations numerically. They do not replace an explanation of the mathematics.
- Typical data
- Tables, models, parameters, simulations, graphs
- Mathematics
- Regression · simulation · numerical methods · optimisation
Example topics
- Nonlinear regression of a cooling curve
- Monte Carlo simulation of Buffon’s needle
- Comparison of sorting or graph algorithms
Practical and safety notes
Search related topics →Document formulas, data ranges, software version and settings. Explain central results rather than presenting black-box output.
d3ee170a-0cd4-40a0-a47d-3cf96c77c05d.jpegSSD, SATA docking station and data backup
What you can do with it
The photographed device is not a sensor; it is a SATA docking station with a KingSpec SSD inserted. It is useful for securely storing, versioning and transferring large video, thermal-image, audio or sensor datasets. A traceable folder structure can be as important as the measuring device.
- Typical data
- Raw data, image sequences, video, audio, scripts, analysis versions
- Mathematics
- Data management · reproducibility · versioning · sample checking
Example topics
- High-frame-rate video of a trajectory
- Thermal-image time series with many frames
- AI classification using a self-collected image dataset
Practical and safety notes
Search related topics →Verify the drive model and backups before initialising or formatting. Keep at least two copies and encrypt or anonymise personal data. The exact dock model is not legible in the photograph.
Equipment is only one part
The mathematical decision remains central.
An expensive sensor does not replace a clear research question or transparent mathematics. A ruler or phone may be enough for a strong paper when experimental design, analysis and reflection are convincing.