Methodology
Every number on this site comes from the formulas on this page. No black boxes: the model, its constants, its sources and — just as important — its limits.
The Speed Estimation Model
The IBO standard rates a bow at 70 lb draw weight, 30″ draw length and a 350-grain arrow with a bare string. The estimator adjusts that rating for the ways a real setup differs, using the three shop rules of thumb that have priced this gap for decades:
- Draw length: ±10 fps per inch away from the reference draw.
- Draw weight (compound): ±2 fps per pound away from 70 lb.
- Arrow weight: ∓1 fps per 5 grains away from the reference arrow weight.
- String accessories: −3 fps for a peep, −4 for peep and D-loop, −6 with silencers fitted.
Recurve and longbow ratings follow a different convention — quoted at a 28″ draw with a reference arrow of 9 grains per pound of draw weight (gpp) — so the same rules are applied from that baseline instead:
Energy and Momentum
Both constants are the standard archery forms of the physics definitions — kinetic energy as ½mv², momentum as mv — with the grains conversions folded in. Unit conversions use the exact definitions: 1 fps = 0.3048 m/s, from which the mph (×0.681818) and km/h (×1.09728) factors follow.
Speed at Distance
Drag spends an arrow's speed at a roughly constant percentage rate. This model spends 1.2% of remaining speed per 10 yards — the middle of the published range for typical hunting arrows — and recomputes kinetic energy at each distance from the reduced speed. It is an approximation: large fletching and light shafts decay faster; heavy, low-drag arrows slower.
FOC and Arrow Weight
FOC follows the standard Easton definition, balance measured from the nock throat on the finished arrow. The weight build-up is a plain sum of published component figures; grains per pound is the total divided by draw weight. The component ranges on the weight page are the makers' published spans for current shafts and parts.
Spine Selection
Static spine is the shaft's measured deflection under the standard test (28″ span, 1.94 lb centre load), expressed in thousandths of an inch. The selection chart groups draw weight and finished arrow length into the common 600 / 500 / 400 / 340 / 300 groups, following the structure of Easton's published shaft-selection charts. Point-weight and cam-aggression adjustments are stated on the spine page itself, and the page says plainly to confirm against your own shaft maker's chart before buying — makers' labels differ at the margins.
Crossbow Adjustment
Crossbow ratings carry no common standard, so the model starts from the maker's own rating and its stated test-bolt weight, then applies the industry rule of one fps per three grains of bolt-weight difference. Energy and momentum are then computed from the adjusted speed with the same formulas as everywhere else on the site.
Limits of the Model
It is an estimate. For a well-tuned compound with honest inputs, expect roughly ±5 fps against a chronograph. Cam design, string condition, tuning state and release consistency all move the real number in ways no adjustment table captures.
Inputs dominate. An IBO rating measured generously, or an arrow weight guessed instead of summed, moves the answer more than any refinement of the model would. The tools are built so the honest input is the easy input.
Traditional bows vary most. Maker ratings for recurves and longbows are not standardised; treat those estimates as ±10 fps territory.
Guidance bands are cited, not invented. The KE, momentum and FOC bands shown across the site reproduce ranges published in manufacturer guidance and the Ashby Bowhunting Foundation's research summaries. They are rules of thumb for well-placed shots with suitable broadheads — never a substitute for local hunting regulations, which always win.
Methodology FAQs
Why does the estimate use 10 fps per inch of draw length?
Because that is the adjustment bow shops and manufacturers’ own tuning guides have used for decades: an inch of draw length adds or removes roughly an inch of power stroke, worth about 10 fps either way around the 30″ IBO reference. It is an approximation — individual bows vary by a few fps per inch — and it is the single biggest term in the model, which is why the estimate is quoted at ±5 fps, not ±1.
Where does the 450,240 constant come from?
Kinetic energy is half mass times velocity squared. Converting grains to pounds (divide by 7,000) and folding in gravitational acceleration to land in foot-pounds produces the single divisor 450,240. It is the standard constant used across archery — the same one in manufacturer KE tables — not a number fitted by this site.
How was the speed-at-distance model chosen?
Arrows lose speed to aerodynamic drag roughly in proportion to their speed, which compounds to a steady percentage loss per distance. The model here — about 1.2% of remaining speed per 10 yards — sits in the middle of published chronograph-at-distance measurements for typical hunting arrows. Light, high-drag arrows (big feathers, light shafts) lose more; heavy, slick arrows lose less. It is labelled an approximation wherever it appears.
Why is the traditional-bow estimate rougher than the compound one?
Compound ratings follow one published test standard (IBO). Traditional bow speeds are quoted by individual makers under their own conditions — usually 28″ draw and 9 grains per pound, but not always, and sometimes with lighter arrows. The model adopts the common convention and says plainly that a trad rating can carry more optimism than an IBO figure.
Can I check the maths myself?
Yes — that is the point of this page. Every formula is printed in full, every constant is named, and the homepage’s worked example can be recomputed by hand in under a minute: 330 − 10 − 10 − 20 − 4 = 286 fps. If your hand calculation and the site ever disagree, the report-an-error page exists for exactly that.
- IBO (International Bowhunting Organization) — the body behind the IBO speed-rating standard: 70 lb, 30 in draw, 350-grain arrow
- Archery Trade Association — industry standards body for bow and arrow measurement (ATA draw length and weight)
- Easton Archery — shaft selection charts — the reference spine-selection and arrow-building charts this site’s groupings follow
- Ashby Bowhunting Foundation — Dr Ed Ashby’s arrow penetration research — the source of the momentum and FOC guidance
- Gold Tip — arrow university and spine charts — manufacturer spine charts and arrow-weight data used to cross-check the tables
- NIST — SI measurement units — the definitions behind the fps to m/s and km/h conversions