Moment Arms, Lever Arms, and Joint Torque: The Physics of Weightlifting Explained Simply

Moment arms in weightlifting come down to one idea: the further a weight sits from a joint, measured at a right angle to the direction of the force, the harder that joint has to work. Joint torque is simply force multiplied by that distance, so the same 10 kg dumbbell can feel easy or brutal depending on where your joints are relative to it.

That is the whole physics lesson. The rest of this guide shows how it plays out in lateral raises, curls, squats and rows, so you can use it when choosing and tweaking exercises. It sits inside our wider exercise selection and biomechanics guide, and no maths is needed beyond one multiplication.

What is a moment arm, in plain gym language?

Take a joint, say your shoulder. Imagine its axis as a bolt your arm swings around. Now hold a dumbbell. Gravity pulls it straight down. The moment arm is the horizontal distance between that bolt and the vertical line of gravity through the dumbbell.

Hang your arm by your side and the dumbbell is almost directly under the shoulder, so the distance is close to zero. Lift your arm until it is level and the dumbbell sits as far out to the side as your arm allows, so the distance is at its largest.

Torque is what that distance turns the weight into:

torque = force x perpendicular distance

A heavier weight raises torque. A longer distance raises torque. Both count equally. This is why a light dumbbell held far from your body can feel worse than a heavy one held close.

How lateral raises show moment arms in action

Lateral raises are the cleanest everyday example, because the weight never changes but the difficulty swings widely.

Here is a quick, illustrative calculation. Say a dumbbell is 8 kg and its centre sits about 0.6 m from your shoulder joint (a made-up but plausible number, and it ignores the weight of your arm). Weight is roughly 8 x 9.81 = 78 N. With your arm level, the perpendicular distance is the full 0.6 m, so torque is around 47 N-m. Raise the arm only to 45 degrees from vertical and the horizontal distance becomes about 0.6 x 0.71 = 0.42 m, so torque drops to roughly 33 N-m. Same dumbbell, about 30% less torque.

This explains two things lifters notice. The bottom of a lateral raise feels almost empty, and the top feels hard. And it is why a cable, which pulls in a different direction, changes where the exercise is hardest. If you want a deeper look at that, see our guide to lateral deltoid training with dumbbells vs cables and machines.

What is the difference between internal and external moment arms?

Every lift involves two levers fighting each other.

• External moment arm: the distance from the joint to the line of the load (dumbbell, barbell, cable).
• Internal moment arm: the distance from the joint to the line of pull of the muscle’s tendon.

For the muscle to hold or lift the weight, its torque must match the load’s torque. Because the internal arm is typically only a few centimetres, while the external arm can be 20 to 60 cm, the muscle has to pull many times harder than the weight itself. That is just a ratio of two distances.

Think of it like a door. Push near the hinge and you need a huge force. Push at the handle and a finger will do. Your biceps is pushing near the hinge, while the dumbbell is hanging off the handle.

Real moment arms are not fixed numbers, either. In ten young men, the moment arms of the biceps, brachialis and brachioradialis at the elbow increased during isometric contractions in most conditions, especially in flexed positions, probably because the muscles thicken when they contract (Akagi et al., 2012). At the knee, the patellar tendon moment arm in ten healthy young people stayed near 46 mm between 0 and 70 degrees of knee flexion and dropped by no more than about 20% at higher flexion angles, with more variation between individuals than between activities (Gray et al., 2021).

Does moment arm length make some people stronger?

A little, but not much. A study compared 16 young men with about four years of heavy knee-extensor training against 52 untrained men. The trained group had about 60% higher knee extension torque and 56% more quadriceps volume, but a patellar tendon moment arm only about 4% larger (Maden-Wilkinson et al., 2020). The authors concluded muscle size was the primary explanation for the strength gap.

So if you have been told your levers are “bad” for a lift, the practical impact is probably modest compared with how much muscle you build. This was a cross-sectional comparison, so it cannot prove training changed the moment arm. It only shows that lever length is not the main driver of strength.

Why small changes in squat position change which joint works

Now apply this to the squat. In a well-balanced squat the bar travels roughly straight up and down over your mid-foot, and your hip and knee are two different bolts. The distance from each bolt to the line of the bar is that joint’s moment arm.

Lean your trunk forward and your hips move back relative to the bar, so the hip moment arm gets longer and the knee’s gets shorter. Stay upright and sit more between your heels, and the opposite happens.

Lab data supports this. In 100 people doing bilateral squats at depths between 60 and 110 degrees of knee flexion, the ratio of hip to knee moment rose with a more forward trunk angle and with a more vertical shank, with trunk angle explaining more of the variance than shank angle (Graber et al., 2023). The authors note this supports using trunk position as a coaching cue to alter hip and knee demands. It is an observational study, so it describes a relationship in those participants, not a guarantee for every body.

What about bar position? A study of 12 recreationally trained men at their 3-rep max found no significant differences in hip, knee or ankle net joint moments between high-bar and low-bar squats when stance width was kept the same, and the loads lifted were similar (Larsen et al., 2024). In other words, bar height alone mattered less than the posture you adopt. Stance width and foot angle also shift joint demands, which we cover in stance width and foot placement for squats and leg press.

Squat vs deadlift: same joints, different loading

In 28 resistance-trained lifters (17 men, 11 women), the deadlift produced a larger hip extensor net joint moment than the back squat (3.59 vs 2.98 Nm per kg), while the squat produced a larger knee extensor moment (2.14 vs 1.18 Nm per kg) (Choe et al., 2021). Those figures were taken at 70 and 85% of each lift’s 1RM.

The deadlift keeps the bar closer to the shins, so the hip carries a long lever while the knee carries a short one. The squat splits the demand more evenly. Neither exercise “isolates” a joint, they simply distribute torque differently. For gym planning, that makes squats or leg presses a sensible knee-dominant choice and hinges a sensible hip-dominant one. For the wider picture, see our look at how body proportions change exercise selection.

Why a bent-over row loads your lower back

The lumbar spine has moment arms too. When you fold forward to row, the weight hangs far in front of your lower back, which creates a long external lever and a large demand on the spinal muscles.

In a laboratory study of seven healthy men comparing three rowing variations, the standing bent-over row produced large activation across the back and the largest lumbar spine load, while the inverted row produced lower lumbar load (Fenwick et al., 2009). The sample was small and healthy, so it is a lab snapshot, not a verdict on any one lifter.

A practical read: if your lower back, not your lats, ends up as the limiting factor in a row, a chest-supported row removes that lever. The back is held up by the pad, and the target muscle does the work. If back pain is persistent, see a doctor or physiotherapist rather than just changing exercises.

How to use moment arms without turning into a physicist

You do not need to calculate anything. Use this short checklist for any exercise:

1. Find the joint you want to train. Elbow for curls, shoulder for lateral raises, knee for leg extensions.
2. Find the line of the load. Gravity pulls straight down on a dumbbell. A cable pulls along the cable.
3. Look at the right-angle distance between the two. Where that gap is biggest, the joint is working hardest.
4. Adjust the setup. Move the weight closer to take load off a joint, or further away to put more on it.

Some examples:

• Preacher vs standing curl: where the forearm sits relative to gravity changes where the biceps meets peak load. We compare them in incline vs preacher curls.
• Holding a dumbbell closer to your body: a shorter external arm means lower torque at that joint.
• Machines and cams: these change the load as the joint moves. See matching resistance profiles to human strength curves.

Common mistakes with moment arms

• Assuming heavier is always harder on the joint. A lighter weight held further out can load a joint more than a heavy one held close.
• Ignoring body-position drift. As you tire, you lean, sway or let the weight drift away from the body, which lengthens the lever and shifts load to joints you did not intend to train.
• Copying someone else’s setup exactly. Limb lengths and tendon attachment sites vary, so an identical-looking position can load you differently. Gray et al. found the knee moment arm varied by as much as 13% from the mean across individuals.
• Using physics to override pain signals. Mechanics can suggest why something hurts, but it cannot diagnose it. Persistent joint pain, numbness or swelling deserves a medical assessment.

Quick reference: what changes the external moment arm

Change	Effect on external moment arm	Example
Move the weight further from the joint	Longer, so higher torque	Lateral raise with a straight vs bent arm
Raise the limb toward horizontal	Longer, so higher torque	Top of a lateral raise
Lean the trunk forward under a bar	Hip arm longer, knee arm shorter	Hinge-style squat
Fold forward unsupported	Lumbar arm longer	Bent-over row
Support the torso	Lumbar arm removed	Chest-supported row

Bending the elbow in a lateral raise shortens the lever, and straightening it lengthens it, a free way to scale difficulty with the same dumbbell.

The bottom line

Moment arms explain a large share of why one rep feels hard and another feels easy: the same weight creates different torque depending on its distance from the joint. External arms are usually long and internal arms short, so muscle forces are far greater than the weight you hold. Small changes in trunk angle, arm angle and support alter which joint carries the load.

Keep it practical. Pick the joint you want to train, look at where the load sits relative to it, and adjust. To put it into a plan, try our free push, pull and leg-day programs, and use the training volume calculator to keep your weekly sets in check.