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Reach Advantage Calculator

See which of two fighters has the longer reach and by how much, plus each fighter's ape index (arm span compared with height), in inches or centimeters.

Level: Grade 6

  • Common Core standard 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
  • Common Core standard 6.RP.A.3.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
  • Common Core standard 6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Printable worksheet

Reach Advantage Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Units

A label only; it never changes the math. Blank shows "Fighter A".

Fingertip to fingertip with the arms straight out to the sides.

A label only; it never changes the math. Blank shows "Fighter B".

Result

Reach advantage

6 in

Fighter A has a 6 in reach advantage.

Reach advantage in cm
15.2 cm
Fighter A ape index (reach − height)
+4 in
Fighter A reach-to-height ratio
1.056
Fighter B ape index (reach − height)
−1 in
Fighter B reach-to-height ratio
0.986
Height difference (Fighter A − Fighter B)
+1 in

See the step-by-step solution ↓

Tale of the tape (in)
Tale of the tape (in)
MeasureFighter AFighter B
Height72 in71 in
Reach76 in70 in
Ape index (reach − height)+4 in−1 in
Reach ÷ height1.0560.986

Step-by-step solution

  1. Reach advantage: the longer reach minus the shorter one (Fighter A has the edge)

    76 in−70 in=6 in
  2. Fighter A's ape index as a difference: reach minus height

    76 in−72 in=4 in
  3. Fighter A's ape index as a ratio: reach divided by height

    76 in72 in=1.0556
  4. Fighter B's ape index as a difference: reach minus height

    70 in−71 in=−1 in
  5. Fighter B's ape index as a ratio: reach divided by height

    70 in71 in=0.9859
  6. The reach advantage in centimeters (1 in = 2.54 cm exactly)

    6×2.54=15.24 cm

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out which of two fighters has the longer reach, and by how much. Reach is one of the first numbers on a tale of the tape, the side-by-side stats shown before a fight. In boxing and MMA it means arm span. It's measured fingertip to fingertip, with the arms held straight out. A longer reach lets a fighter land from a distance where the opponent can't. The calculator tells you who has the edge, in both inches and centimeters.

It also works out each fighter's ape index, the gap between arm span and height. Most people's arm span is close to their height. A positive ape index means longer arms than height alone suggests. The same numbers work for anyone measuring their own wingspan for climbing, swimming or basketball. So the ape index is shown both as a difference and as a ratio.

Where it's used

Why this math matters outside the classroom:

  • Tale of the tape. Fight fans compare a 76 in reach with a 70 in reach and find a 6 in, or 15.24 cm, advantage.
  • Climbing and swimming. Climbers measure a 180 cm arm span against 175 cm of height for an ape index of +5 cm, a ratio of about 1.03.
  • Basketball tryouts. Coaches record players' wingspans alongside height, so a 6 ft 2 in guard with a 6 ft 6 in wingspan has a +4 in ape index.
  • Classroom measurement. Students measure their own arm span and height in centimeters and compare the ratio with 1 to test the idea that they're about equal.
  • Metric fight cards. Broadcasters convert a 193 cm reach to inches by dividing by 2.54, which gives about 76 in.

Grade level and standards: Grade 6; Common Core State Standards for Mathematics 6.RP.A.1, 6.RP.A.3.d, 6.NS.B.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose inches or centimeters, and use the same unit for every measurement.
  2. If you like, type names in place of Fighter A and Fighter B. They only label the results.
  3. Enter each fighter's height and reach (arm span).
  4. Read the reach advantage, who has it, and each fighter's ape index and reach-to-height ratio.

What the inputs mean

Units
1 inch is exactly 2.54 cm. The reach advantage is also shown in the other unit.
Fighter A
A label only; it never changes the math. Blank shows "Fighter A".
Fighter A reach (arm span)
Stand with your back against a wall and your arms straight out to the sides at shoulder height. Measure from the tip of one middle finger to the other. Official fight measurements use the same idea, though methods can differ slightly between organizations.
Fighter B
A label only; it never changes the math. Blank shows "Fighter B".

Formula and method

reach advantage = longer reach − shorter reach
ape index (difference) = reach − height
ape index (ratio) = reach ÷ height
centimeters = inches × 2.54

The reach advantage is the difference between the two arm spans. It's the extra distance, split between both arms, that one fighter can cover without stepping in.

The ape index compares a person's own arm span with their height. As a difference, 0 means arm span equals height. A positive number means longer arms, and a negative one means shorter arms. As a ratio, 1 means equal, and above 1 means longer arms. Both versions are in common use, so both are shown.

A fighter can be shorter and still have the longer reach. That's why the height difference is listed separately.

Worked example

Two made-up fighters: Fighter A is 72 in tall with a 76 in reach, and Fighter B is 71 in tall with a 70 in reach.

  1. Reach advantage: 76 − 70 = 6 in, to Fighter A. In centimeters: 6 × 2.54 = 15.24 cm.
  2. Fighter A's ape index: 76 − 72 = +4 in, or 76 ÷ 72 = 1.056.
  3. Fighter B's ape index: 70 − 71 = −1 in, or 70 ÷ 71 = 0.986.
  4. Fighter A is also 1 in taller, but most of the reach edge comes from longer arms, not height.

Result: Fighter A has a 6 in reach advantage.

Understanding the result

A few inches of reach can matter. That's especially true for a fighter who likes to work behind a jab, or kick from a distance. But it's only one factor. Footwork, timing and the opponent's style decide whether a reach edge turns into landed strikes.

An ape index near zero is typical. Values a few inches either way are common. Larger positive values often get noticed in sports that reward long arms.

Assumptions and limitations

  • Reach means full arm span, fingertip to fingertip. Height is standing height without shoes.
  • Both fighters are measured in the same unit.
  • Published reach figures come from different measuring methods. They're sometimes rounded or out of date.
  • Leg reach for kicks isn't measured.
  • The ape index only describes body proportions. It says nothing about health.

Frequently asked questions

Is reach the same as wingspan?

In combat sports, yes. Reach is the arm span from fingertip to fingertip, with the arms spread. Some people use reach to mean how far one arm extends. That's roughly half the span plus the shoulder width. But fight cards use the full span.

What is a good ape index?

There's no good or bad value. It just describes body proportions. Most people are within a few inches of zero. A positive value means arm span is longer than height. That can help in sports where reaching farther is an advantage.

Can a shorter fighter have a longer reach?

Yes. Reach depends on arm length and shoulder width, not just height. Picture a 70 in fighter with a 74 in reach, facing a 72 in fighter with a 72 in reach. The shorter fighter has a 2 in reach advantage.

How do I convert reach between inches and centimeters?

Multiply inches by 2.54 for centimeters, or divide centimeters by 2.54 for inches. A 76 in reach is 193.04 cm.

How this calculator is checked

Method: Direct differences and ratios of arm span and height (ape index as reach − height and as reach ÷ height); exact inch–centimeter factor. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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