How our numbers are made
Every figure on MathBikes has a formula behind it. This page documents exactly how each calculator works, where our constants come from, and the limits of what a model can tell you - because we'd rather be honestly approximate than precisely wrong.
Our core principle
Marketing numbers are designed to sell; ours are designed to decide. We publish open formulas, calibrated constants and honest ranges so you can check our working and trust the output. If a number can't be defended, we don't print it.
Range: watt-hours ÷ adjusted consumption
Range starts from a simple division - battery capacity in watt-hours (Wh) divided by energy used per kilometre. Base consumption is set by assist level (Eco ≈ 7, Tour ≈ 11, Sport ≈ 15, Turbo ≈ 20 Wh/km), then multiplied by transparent factors for terrain (flat 1.0 → steep 1.6), rider and cargo weight (±1% per 5 kg from an 80 kg baseline), tyres (road 1.0 → knobby 1.25), temperature (mild 1.0, cold 1.2) and pace or wind (relaxed 0.9 → fast/headwind 1.3). We then show a ±12% band rather than a single figure, because real-world variance genuinely lives in that range.
The range figure on each bike page
The calculator above answers "how far will it go for me". Each bike page answers a narrower question: how far would this bike go for a standard rider on a standard ride, so that two bikes can be compared on the same terms. That reference ride is the calculator's own defaults - Tour assist, rolling terrain, mild weather, brisk pace, an 80 kg rider - and you can reproduce any published figure by dialling those in. The only things that change between bikes are the ones that belong to the bike: battery capacity, weight, and tyres inferred from the bike's type, because knobby tyres cost around a quarter of the range and no catalogue we can reach lists tyres directly.
Why the estimate sits well below the claim
Manufacturer ranges are quoted in the best case: lowest assist, flat ground, light rider, no wind. Our reference ride is a normal one. Across the catalogue the estimate lands at roughly half the claimed figure, and that gap is the difference between two sets of conditions, not an accusation. Where you ride in Eco on the flat, your real range will be closer to the claim than to our number - which is exactly what the calculator is for.
When we publish no range at all
The catalogue is scraped, and scraped numbers go wrong in ways that look confident. Six bikes list 2,080 to 3,120 Wh, which is around three times what fits on a bicycle; one lists a weight of 2.7 kg; a few would need a battery pack heavier than the frame it sits in. Those eleven bikes show no estimate, because publishing one would put our name on a supplier's typing error. We would rather show a gap than fill it.
What our range estimate cannot tell you
It is a model, not a measurement, and it inherits the quality of what goes into it. Weight is the weakest input: when we checked the original 286-bike catalogue, 89 were listed at exactly 22.7 kg, which is the round 50 lb figure suppliers publish rather than a weighed number. Tyres are inferred from the bike's type, so a road-tyred fat bike is scored as if it had knobbies. Motor efficiency, controller behaviour, battery age and cell quality are not in the formula at all. Treat the figure as a fair basis for comparing bikes with each other, and the calculator as the way to estimate your own ride.
Savings: full cost per kilometre
We compare what you actually spend per replaceable kilometre against an e-bike's running cost. Car cost per km includes fuel (your consumption × fuel price), plus EU-average maintenance (€0.06), depreciation (€0.12) and parking (€0.02). E-bike running cost is electricity (≈15 Wh/km × your tariff) plus €0.04/km maintenance and a €100/year service allowance. Annual savings, payback period and a five-year cumulative position fall out of that.
Total cost of ownership
TCO projects the full cost of owning a bike over your chosen years: purchase price, plus charging, plus maintenance (hub motors ≈ €120/yr, mid-drives ≈ €180/yr), plus battery replacement when lifetime kilometres are exceeded (≈ €1.20 per Wh), minus an estimated resale value that decays from 60% with an 18%/year curve and a 15% floor.
Battery economics
Lifetime kilometres ≈ rated charge cycles × kilometres per charge. Cost per kilometre is the replacement price divided by that lifetime, and the likely replacement year is lifetime kilometres divided by your annual distance. Our degradation curve assumes capacity falls toward a ~70% end-of-life threshold - the point most riders notice a meaningful range drop.
Finance
Monthly payments use standard amortization - M = P·r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is the amount financed, r is the monthly rate (APR ÷ 12) and n is the term in months. We show total interest and the principal/interest split so the true cost of credit is visible.
Estimated vs claimed range
For every bike with enough published data, we set the manufacturer's claimed range beside our estimate for a standard reference ride, worked out with the formula on this page. Across the catalogue the estimate lands at roughly half the claim, and we always display the gap. It is a computed figure, not a test: we have not ridden these bikes.
Legal class: how we check a bike against the law
Each e-bike law page counts our catalogue against that market's bicycle class. A bike counts as over the limit when its listed top speed is above the class's assisted-speed limit (25 km/h in the UK, the EU and Australia, 32 km/h in Canada, 28 mph in the US), or when it is flagged as a 45 km/h fast class where that is not a bicycle. A missing top speed, or a throttle the listing cannot show stops in time, counts as not enough data. Motor power joins the check once the catalogue stores rated power. A listing is not a legal classification: the label on the bike and the law decide, and every rule on those pages links to its source.
Where our constants come from
Defaults are EU averages drawn from public energy pricing, manufacturer specifications and our own modelling. They're starting points, not gospel: every calculator lets you override them with your own local figures for a more accurate result.
Electricity prices
The calculators start from the average household electricity price of the market you browse in, and the bike pages price charging with it. Each figure is read from the publisher named beside it, copied as published, and dated; where no official figure could be read we show none and fall back to a euro default, which every calculator lets you overwrite.
| Market | Price | Covers | Source |
|---|---|---|---|
| United States | $0.173 per kWh | average residential retail price in the United States, taxes and fees included (17.30 cents per kWh); 2025, annual average. | U.S. Energy Information Administration (Electric Power Monthly, Table 5.3), U.S. Energy Information Administration (what the price includes) (read 9 October 2026) |
| Europe | €0.2896 per kWh | EU-27 average household price, band DC (2,500 to 4,999 kWh a year), all taxes and levies included; second half of 2025. | Eurostat (dataset nrg_pc_204, band DC) (read 9 October 2026) |
| United Kingdom | £0.2632 per kWh | Ofgem price cap unit rate for electricity, Direct Debit, Great Britain average, no VAT on electricity in this period (26.32 pence per kWh, standing charge not included); 1 October to 31 December 2026, price cap period. | Ofgem (price cap rates) (read 9 October 2026) |
| Canada | None. Calculators start at 0.30 EUR, converted. | Canada has no national tariff. The Canada Energy Regulator publishes provincial prices only as a chart, without taxes, and states no national average. We found no official city or national figure we could read, so we show none. | Canada Energy Regulator (provincial prices) (read 9 October 2026) |
| Australia | None. Calculators start at 0.30 EUR, converted. | Australian prices differ by state and network. The AEMC's price report is a projection drawn in charts without a figure, and we found no national average on an official source we could read, so we show none. | Australian Energy Market Commission (price outlook) (read 9 October 2026) |
Limits and honesty
A model is a map, not the territory. Weather, tyre pressure, battery age, individual riding style and local pricing all move the real number. Our outputs are calibrated estimates for guidance, not guarantees - treat them as a well-reasoned starting point, then verify anything mission-critical with a test ride.
Corrections
Found a constant you think is off, or a result that doesn't match your experience? We want to know. Email [email protected] with the details and we'll review the model - accuracy is the entire product.
