Sagitta shows up in more places than most people realize — mountain bike suspension tuning, satellite dish geometry, optical lens design, and the gentle arc of a curved beam all rely on the same measurement. A sag calculator finds that arc height quickly, whether you're setting up rear shock sag on a dirt bike or calculating the curvature of a架构 panel.

For suspension work specifically, sag percentage tells you whether your spring rate and preload are dialed in correctly for your weight and riding style. For engineering and architectural applications, sagitta describes how far a curved surface departs from a straight line across a given span. This guide covers both applications, walks through four real worked examples, and explains exactly how to read your results.

What Is a Sag Calculator and Why Does It Matter?

A sag calculator determines the sagitta, meaning the height of an arc's curve measured from the midpoint of its chord to the arc itself, or in suspension terms, the amount a spring compresses under load. It works using the geometric relationship between a circle's radius, chord length, and arc height, or for suspension, a simple percentage of total travel. Engineers, machinists, and mountain bike or motocross riders all use this calculation regularly. Getting suspension sag wrong means harsh, unpredictable handling; getting structural sagitta wrong means a curved component that doesn't fit its intended radius.

What You Need Before You Start

Gather the right measurements depending on which type of sag you're calculating.

For suspension: your bike or vehicle's total available travel in millimeters or inches.
For suspension: the measured sag distance with the rider or load in normal riding position.
For geometric sagitta: the chord length, the straight-line distance across the arc's base.
For geometric sagitta: either the radius of the curve or the arc height if radius is unknown.
Whether you're measuring static sag or race sag, since these use different measurement conditions.
The units your project specification calls for, since suspension work often mixes millimeters and inches.

How to Use This Sag Calculator — Step by Step

Choose your calculation type first, then enter the relevant measurements for accurate results.

Select whether you need suspension sag percentage or geometric sagitta.
For suspension, enter total travel and measured sag distance.
For geometric sagitta, enter chord length and either radius or arc height.
Confirm your unit of measurement matches your input values.
Review the calculated sag percentage or sagitta height.
Compare your result against the recommended range for your application.
Adjust spring preload or curve dimensions based on where your result falls.

The Sag Calculator Formula — Explained Simply

For suspension applications, sag percentage simply divides how far the suspension compresses under load by its total available travel. For geometric applications, sagitta uses circle geometry to find how far an arc bulges away from a straight chord line.

Suspension Sag % = (Measured Sag ÷ Total Travel) × 100 Geometric Sagitta = R − √(R² − (C/2)²)

Measured Sag — the compression distance under load, in millimeters or inches, typically 10 to 50mm on motocross suspension.
Total Travel — the full available suspension stroke, typically 100 to 300mm depending on the vehicle type.
R — the radius of the circle forming the arc, in any consistent unit, typically inches or millimeters for machining applications.
C — the chord length, the straight-line distance across the base of the arc.
Sagitta — the resulting arc height, always smaller than the radius itself.

The suspension formula works because sag percentage is just a straightforward ratio of two measured distances, giving riders a standardized way to compare setups across different bikes. The geometric sagitta formula comes from the Pythagorean theorem applied to circle geometry, a widely accepted mathematical relationship used across machining, optics, and structural engineering wherever curved surfaces need precise dimensioning.

Sag Calculator — Worked Examples

Beginner Example: Mountain Bike Rear Shock Sag Setup

A rider is setting up race sag on a mountain bike with 130mm of total rear travel, and after sitting on the bike in riding gear, a friend measures 33mm of shock compression.

Divide measured sag by total travel: 33 ÷ 130 = 0.254.
Convert to percentage: 0.254 × 100 = 25.4 percent.
Compare against the typical trail-riding target range of 25 to 30 percent sag.

This rider's 25.4 percent sag sits right at the low end of the recommended range for trail riding, meaning the setup leans slightly firm but stays within acceptable limits. If the rider wants a plusher feel for rough terrain, reducing spring preload slightly would push sag closer to 28 or 30 percent.

Professional Example: Motocross Race Sag Fine-Tuning

A professional motocross mechanic is dialing in race sag for a rider on a bike with 315mm of total rear wheel travel, targeting the sport-specific 100 to 105mm sag range, and the initial measurement comes back at 118mm.

Divide current measured sag by total travel: 118 ÷ 315 = 0.375.
Convert to percentage: 0.375 × 100 = 37.5 percent, well above the target range.
Calculate the target sag distance instead: 315 × 0.33 (33 percent, mid-range target) = 103.95mm.
Determine the adjustment needed: 118mm minus 103.95mm equals 14.05mm too much sag.

The mechanic needs to increase spring preload to reduce sag by roughly 14mm, bringing the setup from an overly soft 37.5 percent down to the sport-correct 33 percent range. Motocross demands firmer sag than trail mountain biking because race terrain includes hard landings that would bottom out a softer setup.

Edge Case: Sagitta for a Curved Structural Panel

A fabricator needs to calculate the sagitta for a curved metal panel with a 15-foot radius and a chord length of 8 feet, an unusual application where the panel's curve must match an architectural specification exactly.

Calculate half the chord length: 8 ÷ 2 = 4 feet.
Square the half-chord: 4² = 16.
Square the radius: 15² = 225.
Subtract: 225 − 16 = 209.
Take the square root: √209 = 14.457 feet.
Subtract from radius to find sagitta: 15 − 14.457 = 0.543 feet, or about 6.5 inches.

This fabricator needs the panel to bulge 6.5 inches away from a straight line across its 8-foot chord to match the specified 15-foot radius exactly. Because architectural panels need precise curvature to align with adjacent sections, this sagitta value becomes the target measurement checked during fabrication and installation.

Regional/Metric Example: European Optical Lens Sagitta

An optics technician in Germany needs to calculate the sagitta for a lens surface with a 250mm radius of curvature and a 60mm lens diameter, following standard optical industry practice for lens grinding specifications.

Chord length equals lens diameter: 60mm.
Calculate half the chord: 60 ÷ 2 = 30mm.
Square the half-chord: 30² = 900.
Square the radius: 250² = 62,500.
Subtract: 62,500 − 900 = 61,600.
Take the square root: √61,600 = 248.193mm.
Subtract from radius to find sagitta: 250 − 248.193 = 1.807mm.

This technician needs the lens surface to depart from flat by exactly 1.807mm at its center compared to the edge, a precise specification that lens grinding equipment uses directly for surface calibration. Optical applications like this require sagitta precision to three decimal places, far tighter tolerance than typical construction or automotive sag calculations.

Sag Calculator Results — What the Numbers Mean

For suspension applications, your sag percentage tells you immediately whether your setup runs soft, firm, or balanced. A low result, under 20 percent, means the suspension barely compresses under normal load, producing a harsh ride and reduced traction on rough terrain. A high result, above 35 percent, means the suspension sits too deep in its travel already, risking harsh bottoming on impacts and vague, wallowy handling.

The normal range depends heavily on application: trail mountain biking typically targets 25 to 30 percent, while motocross and off-road racing usually targets a firmer 30 to 34 percent to handle harder impacts. Road and gravel bikes often run less sag overall, closer to 15 to 20 percent, since they encounter smaller bumps.

The most common misunderstanding people have is assuming a single universal sag target applies across all riding disciplines, when the correct target actually depends entirely on your bike type, riding style, and terrain. What you should do differently based on your result is treat the standard range as a starting point, then fine-tune within it based on how the bike actually feels on your specific terrain, since two riders at the same body weight can prefer noticeably different sag settings.

For geometric sagitta, the result simply confirms your curve's departure from flat, and there's no "good" or "bad" range since it depends entirely on your design specification.

How Your Inputs Change the Result

Total travel has a major effect on suspension sag percentage because it's the denominator in the calculation. The same 30mm of measured sag represents 23 percent on a bike with 130mm travel but only 15 percent on a long-travel enduro bike with 200mm travel, so comparing raw sag distances between different bikes without accounting for travel is misleading.

Chord length versus radius interact in a way that surprises people new to geometric sagitta. Doubling the chord length on a fixed radius more than doubles the sagitta, since the relationship isn't linear — it grows faster as chord length approaches the full diameter of the circle.

Spring preload adjustments shift measured sag inversely, meaning more preload reduces sag while less preload increases it, but the relationship isn't perfectly linear because spring rate and leverage ratio both influence how much a given preload change actually moves the sag number.

Here's how radius affects sagitta for a fixed 6-foot chord length, showing how much curve depth changes as radius increases:

Radius (ft) | Sagitta (ft) | Sagitta (inches) 8 | 1.23 | 14.7 12 | 0.78 | 9.4 20 | 0.46 | 5.5 40 | 0.23 | 2.7

Rider weight and gear affect suspension sag directly since more load compresses the spring further, which is why professional setup always measures sag with the rider in full gear, not just body weight alone on a scale.

Sag Calculator — Common Mistakes to Avoid

Measuring suspension sag without full riding gear. Skipping boots, pads, and hydration pack weight during measurement produces a sag number that doesn't reflect actual riding conditions, throwing off the entire setup.
Confusing static sag with race sag. Static sag measures the bike's own weight only, while race sag includes the rider, and using one measurement method when the specification calls for the other leads to an incorrectly tuned suspension.
Applying suspension sag targets to geometric sagitta problems. These are two completely different calculations sharing only a name, and mixing up percentage-based suspension targets with radius-based geometric formulas produces meaningless results.
Using inconsistent units within the geometric sagitta formula. Entering chord length in inches while radius is in feet without converting first produces a wildly incorrect sagitta value.
Forgetting that sagitta always assumes a true circular arc. Surfaces with a parabolic, elliptical, or otherwise non-circular curve need a different formula entirely, and applying the circular sagitta equation to those shapes introduces measurable error.
Ignoring leverage ratio differences between bikes when comparing sag. Two bikes with identical wheel travel numbers can have very different shock stroke and leverage ratios, meaning the same percentage sag doesn't always feel equivalent between them.
Rounding chord or radius too early in multi-step sagitta calculations. Small rounding errors early in the square-and-subtract process compound into a noticeably wrong final sagitta on precision applications like optics.
Treating a single sag measurement as final. Suspension settles and seals break in over time, so a sag measurement taken on a brand-new bike can drift after the first several rides, requiring a recheck.

Key Terms Explained

Sagitta

The height of an arc measured from the midpoint of its chord to the highest point of the curve itself.

Chord

The straight line connecting the two endpoints of an arc, forming the base from which sagitta height is measured.

Radius of Curvature

The distance from the center of a circle to any point on its edge, defining how tightly or gently an arc curves.

Sag Percentage

In suspension terms, the ratio of measured compression to total available travel, expressed as a percentage.

Static Sag

Suspension compression measured from the bike's own weight alone, without a rider seated or standing on it.

Race Sag

Suspension compression measured with the rider in full riding position and gear, reflecting actual riding load.

Preload

The initial compression set on a spring before any riding load is applied, adjusted to fine-tune sag percentage.

Leverage Ratio

The mechanical relationship between rear wheel travel and shock stroke, which affects how sag percentage translates to actual wheel movement.

How This Calculator Works — Methodology

This calculator applies two distinct methods depending on application. Suspension sag uses a straightforward percentage calculation dividing measured compression by total travel, following conventions established across the motocross and mountain bike industries through decades of suspension tuning practice. Geometric sagitta applies the Pythagorean theorem to circular arc geometry, a mathematical relationship with no single named standard body but universally used across machining, optics, and structural fabrication.

The calculation assumes a true circular arc for geometric sagitta, meaning parabolic or elliptical curves fall outside its scope and need different formulas. Suspension sag assumes accurate manual measurement at the shock or fork, since the calculator can't verify measurement technique. Results round to one decimal place for percentages and to three decimal places for precision sagitta applications like optics.

Frequently Asked Questions About Sag Calculator

1. What does a sag calculator actually calculate?

It calculates either suspension sag percentage, showing how much a spring compresses under load relative to total travel, or geometric sagitta, showing how far a curved arc departs from a straight chord line. Which calculation applies depends entirely on which type of sag you select.

2. How accurate is a sag calculator's result?

Geometric sagitta is mathematically exact once you enter accurate radius and chord measurements. Suspension sag accuracy depends entirely on careful manual measurement technique, since the formula itself is a simple, error-free ratio calculation.

3. What is the sagitta formula in simple terms?

Take your circle's radius, subtract the square root of the radius squared minus half the chord squared, and that result is your sagitta height. It's essentially the Pythagorean theorem applied to a curved arc instead of a straight triangle.

4. Does sag terminology differ between suspension and engineering applications?

Yes, suspension sag refers to a percentage of travel compressed under load, while engineering sagitta refers to a specific linear measurement of arc curvature. Both share the word sag or sagitta but describe completely different physical measurements.

5. When does this calculator not apply?

Suspension sag calculations don't apply to air spring systems using different tuning methods like air pressure charts, and geometric sagitta doesn't apply to non-circular curves like parabolic or elliptical arcs. Both situations need different specialized approaches.

6. How can I get a more precise sag result?

For suspension, measure sag multiple times with consistent rider position and gear, then average the results for accuracy. For geometric sagitta, use precise radius and chord measurements to at least three decimal places, especially for optics or precision machining work.

7. What's a typical sag percentage for trail mountain biking?

Most trail mountain bikes target 25 to 30 percent sag for a balance of small-bump sensitivity and support during harder impacts. Cross-country bikes often run slightly less, around 20 to 25 percent, favoring pedaling efficiency over plushness.

8. Should I consult a professional for suspension setup?

Basic sag setup is straightforward enough for most riders to handle themselves with a shock pump and a helper. For advanced tuning involving compression and rebound damping, or for competitive racing setups, a professional suspension tuner can fine-tune beyond basic sag percentage alone.

Related Calculators Worth Bookmarking

Spring Rate Calculator — figure the correct spring rate for your rider weight before fine-tuning sag percentage.
Roof Pitch Calculator — apply related arc and angle geometry concepts to roofline curvature and slope calculations.
Beam Load Deflection Calculator — compare structural sag under load to suspension sag concepts in a different engineering context.
Circle Calculator — calculate additional circle properties like circumference and area alongside your sagitta measurement.
Arc Length Calculator — find the curved distance along your arc as a companion measurement to sagitta height.
Gear Ratio Calculator — useful for motocross and mountain bike setups where drivetrain tuning pairs with suspension sag adjustment.
Tire Pressure Calculator — another key suspension-adjacent setting that affects overall ride feel alongside sag percentage.
Radius Calculator — solve for radius directly if you know sagitta and chord length but need the reverse calculation.

References and Further Reading

American Motorcyclist Association. Motocross Suspension Setup Guidelines. AMA, 2020.
International Mountain Bicycling Association. Suspension Setup and Trail Riding Fundamentals. IMBA, 2019.
Society of Automotive Engineers. Vehicle Dynamics Terminology (SAE J670). SAE International, 2008.
Optical Society of America. Handbook of Optics: Fundamentals, Techniques, and Design. Optica Publishing Group, 2018.

Important Disclaimer

This calculator is for informational and educational purposes only. It does not constitute engineering or safety advice. Always consult a qualified suspension technician or structural engineer before finalizing safety-critical suspension setups or load-bearing curved structural components.