How our numbers are made

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.

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.

Tested vs claimed range

Where we can, we compare a manufacturer's claimed range with a standardized real-world estimate under mixed conditions. The gap is typically 30–40%, and we always display it. This proprietary tested figure is the data we're proudest of - and the figure marketing departments least want you to see.

Where our constants come from

Defaults are EU averages drawn from public energy pricing, manufacturer specifications, independent range testing 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.

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 info@mathbikes.com with the details and we'll review the model - accuracy is the entire product.