Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

What is the best tilt for a solar panel at my home?

AA SLAI SLAA HLAI HL Solid Also in: Calculus, Geometry & Voronoi

Research question

How does the annual energy from a solar panel at my location depend on its tilt angle, and how much extra energy would adjusting the tilt each season provide?

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Why it makes a good exploration

The common rule “tilt equals latitude” is only approximate. Modelling output against tilt, and checking with PVWatts, gives an answer for your own roof.

The mathematics you'll need

Trigonometric model of sunlight on a tilted surface
Summing or integrating over the year
Maximising a function of tilt
Comparing with simulated output data

Modelling the data, step by step

This idea usually needs a sinusoidal model. See it worked step by step, with a criterion tip at every step: Sinusoidal y = a sin(b(x − c)) + d.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

Where the data comes from

Run PVWatts for your location at a range of tilts; use sun-elevation data for your own model.

PVWatts Calculator — Estimated monthly solar-panel output for any location, tilt and orientation.
timeanddate.com sun calculator — Sunrise, sunset and day length for any city and date.

A possible outline

Explain why tilt matters.
Build a simple model from sun elevation.
Find the optimal fixed tilt.
Compare with PVWatts results.
Model seasonal adjustment and reflect on clouds and diffuse light.

Pitfalls that cost marks

Ignoring diffuse light and weather.
Mixing degrees and radians.
Treating PVWatts output as measured data.

Showing personal engagement

Use your own home's location and roof angle.
Estimate the money saved.
Compare with a friend in another country.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Trigonometric model of sunlight on a tilted surface; Summing or integrating over the year
AA HL	Good fit	Trigonometric model of sunlight on a tilted surface; Summing or integrating over the year
AI SL	Good fit	Trigonometric model of sunlight on a tilted surface; Summing or integrating over the year
AI HL	Good fit	Trigonometric model of sunlight on a tilted surface; Summing or integrating over the year

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: ignoring diffuse light and weather; and mixing degrees and radians. Say how each one affects your answer.

Use of mathematics (E)

SL: trigonometric model of sunlight on a tilted surface; summing or integrating over the year; maximising a function of tilt; comparing with simulated output data, each explained in your own words and carried out correctly.

How environment explorations reach the top bands in general: Environment & climate IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Compare the optimum for maximising annual output with the optimum for maximising winter output.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL environment exploration adds.

See a complete IA, marked

When is the sea warm enough for our swimming club? A sinusoidal model of sea temperature (AI SL) is a complete environment exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AI SL, AA HL and AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Trigonometric model of sunlight on a tilted surface, summing or integrating over the year, maximising a function of tilt and comparing with simulated output data.

Where can I get data for this IA?

Run PVWatts for your location at a range of tilts; use sun-elevation data for your own model. Checked sources and tools: PVWatts Calculator and timeanddate.com sun calculator.

Turn this idea into your IA

The planner opens with “What is the best tilt for a solar panel at my home?” filled in: the question, the maths and the data sources.

Plan this IA free

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