Lander Formula: Complete Guide

Lander formula 1RM notation card showing the linear equation one rep max equals 100 times weight divided by 101.3 minus 2.671 times reps, developed by Tom Lander in 1985.

The Lander formula is the most conservative in the calculator at 1-9 reps and uniquely the most accurate of all seven at a single-rep input, but it crosses above Epley at exactly 9.4 reps and turns aggressive at high rep counts. That inverse trajectory, conservative at the start, aggressive by the end, sets it apart from every other formula here. This guide covers the notation, worked examples, exactly where the crossover happens, and the hard limit where it stops working entirely.

At a Glance

  • Formula: 1RM = (100 × w) ÷ (101.3 − 2.671 × r)
  • Type: Linear, the denominator is a straight line, unlike exponential Mayhew or Wathan
  • At r=1: The most accurate formula in the engine, returning 101.4 kg from a 100 kg input (a 1.4% overestimate, versus Mayhew’s 8.9%)
  • At 1-9 reps: More conservative than Epley, useful as a safe programming floor
  • At 9.4 reps: Crosses Epley exactly, the point where the two formulas equalize
  • At 10+ reps: More aggressive than Epley; matches Brzycki from 12+ reps
  • Hard limit: Breaks down at r≈38, where the denominator hits zero
  • Developed by: Tom Lander (1985, NSCA Journal)

What Is the Lander Formula?

The Lander formula uses a linear denominator to predict maximum strength from a submaximal multi-rep set. Unlike the additive formulas (Epley) or the exponential ones (Mayhew, Wathan), the denominator here is simply a straight-line function of rep count, which makes it transparent and easy to reason about but also creates a hard breakdown point at high rep counts.

The Notation and Plain English

Formula notation:

1RM = (100 × w) ÷ (101.3 − 2.671 × r)

In plain English: multiply your weight by 100, then divide by the result of subtracting 2.671 times your rep count from 101.3.

Step by step:

  1. Multiply your rep count (r) by 2.671
  2. Subtract that from 101.3 to get the denominator
  3. Multiply your weight (w) by 100
  4. Divide step 3 by step 2 for your estimated 1RM

Lander quick reference, 100 kg input at key rep counts:

Reps (r)DenominatorLander 1RMEpley 1RMDifference
198.6101.4 kg103.3 kgLander −1.9 kg
393.3107.2 kg110.0 kgLander −2.8 kg
587.9113.7 kg116.7 kgLander −3.0 kg
879.9125.1 kg126.7 kgLander −1.6 kg
1074.6134.1 kg133.3 kgLander +0.8 kg
1269.3144.4 kg140.0 kgLander +4.4 kg
1561.3163.3 kg150.0 kgLander +13.3 kg

The gap narrows as reps approach 9.4, the crossover point. Past it, Lander progressively overtakes Epley.

Why a Linear Denominator?

The linear structure (101.3 − 2.671r) means each rep subtracts a fixed 2.671 from the denominator, unlike Mayhew and Wathan’s exponential decay or Epley’s additive scaling. That makes the formula easy to compute by hand, but it carries a consequence: when r reaches 101.3 ÷ 2.671 ≈ 37.9, the denominator hits zero and the estimate goes infinite. Past r=38, the denominator turns negative and the formula breaks entirely, a reflection of the computational constraints of pre-calculator strength coaching in 1985.

Who Developed the Lander Formula?

Tom Lander published the formula in the NSCA Journal in 1985, the same year Boyd Epley published his own additive formula, both part of the same generation of research seeking to eliminate the need for dangerous maximal tests. Lander’s paper, “Maximum based on reps” (NSCA J. 1985;6(6):60-61), introduced the linear denominator approach used here. Some online sources incorrectly attribute this formula to Lyle McDonald. The calculator uses Tom Lander’s 1985 equation specifically, not any formula from Lyle McDonald, whose work describes different approaches to 1RM estimation with different structures and constants entirely

Lander Formula: Worked Examples

Example 1: Conservative Low-Rep Input, 80 kg × 3 Reps

Calculation:

1RM = (100 × 80) ÷ (101.3 − 2.671 × 3) = 8,000 ÷ 93.29 = 85.8 kg

Comparison: Epley gives 88.0 kg. Lander runs 2.2 kg more conservative, meaning working percentages come in slightly lighter, reducing overreach risk in a new training block.

Example 2: Mid-Range Input, 120 kg × 8 Reps

Calculation:

1RM = (100 × 120) ÷ (101.3 − 2.671 × 8) = 12,000 ÷ 79.93 = 150.1 kg

Comparison: Epley gives 152.0 kg. Lander runs 1.9 kg more conservative, and at 8 reps the two are converging toward the crossover at 9.4, so the gap is nearly closed. Both are usable here; Lander stays the slightly safer estimate.

Lander vs the Other 6 Formulas: The Full Comparison

Lander traces a U-shaped relationship against the field: most conservative at low reps, crossing Epley at 9.4, then second-most-aggressive at 12+ reps, behind only Brzycki, which it nearly matches.

RepsLanderEpleyBrzyckiMayhewLombardiO’ConnerWathan
3107.2 kg110.0 kg105.9 kg114.0 kg111.6 kg107.5 kg109.0 kg
5113.7 kg116.7 kg112.5 kg119.0 kg117.5 kg112.5 kg116.6 kg
8125.1 kg126.7 kg124.1 kg126.3 kg123.1 kg120.0 kg127.7 kg
10134.1 kg133.3 kg133.3 kg130.9 kg125.9 kg125.0 kg134.7 kg
12144.4 kg140.0 kg144.0 kg135.4 kg128.2 kg130.0 kg141.5 kg
15163.3 kg150.0 kg163.6 kg141.7 kg131.1 kg137.5 kg150.9 kg

Bold marks where Lander sits above Epley (10+ reps). At 3-9 reps, Lander runs below Epley; past 9.4 reps it overtakes it.

The 9.4-Rep Crossover: Where Lander Turns Aggressive

At r=9.4, Lander and Epley both land at roughly 131.2-131.3 kg, virtually identical. Below that point, Lander is the more conservative choice. Above it, Lander turns more aggressive and the gap widens quickly: at 12 reps it’s 4.4 kg above Epley, at 15 reps it’s 13.3 kg above. That’s not a flaw, it reflects the mathematical trajectory of the linear denominator, but it’s a real consideration for anyone estimating from a high-rep set. Lander shouldn’t be used with inputs above 10 reps. For the additive formula it’s crossing, see Epley Formula: Complete Guide, and for how this crossover connects to rep-max conversion generally, see Rep Max Equivalency.

Line chart showing the full trajectory of the Lander formula against Epley across rep counts, conservative from 1 to 9 reps, crossing at 9.4 reps, becoming increasingly aggressive from 10 to 20 reps, and approaching a mathematical breakdown as reps near 38.
Lander runs below Epley through 9 reps, crosses at exactly 9.4, then climbs increasingly aggressive before the denominator approaches zero near 38 reps.

The Brzycki Convergence at 12+ Reps

At 12 reps, Lander (144.4 kg) and Brzycki (144.0 kg) are virtually identical. At 15 reps, they give 163.3 kg versus 163.6 kg, indistinguishable from any practical standpoint. Both use a linear denominator structure (Brzycki’s equivalent is 36 ÷ (37−r)), and both converge to the same aggressively high estimates at high rep counts. That shared structure explains the convergence and confirms that neither Lander nor Brzycki should be used with 12+ rep inputs for 1RM estimation.

How Accurate is the Lander Formula?

Lander was included in the LeSuer et al. (1997) validation study that tested seven formulas across all three competition lifts. Like every formula in that study, it showed a correlation greater than 0.95 with actual 1RM, though correlation alone doesn’t guarantee small absolute errors. Lander’s accuracy is best read by rep range.

Accuracy at a glance:

  • At r=1: The most accurate formula in the engine, outputting 101.4 kg from a 100 kg input (a 1.4% overestimate), closer to the theoretically correct value than any other formula at this rep count
  • At r=3-9: Conservative estimates within ±2-3 kg below Epley, reliable for programming and unlikely to overload training percentages
  • At r=10-12: A growing gap above Epley, 0.8-4.4 kg higher in this range, moderate reliability only
  • At r=15+: Significant overestimation, 13+ kg above Epley; don’t program from this range

For the broader validation research across all 7 formulas and how Lander’s accuracy fits the wider picture, see How Accurate Are 1RM Calculators?

Limitations of the Lander Formula

  • Breaks down above r≈37.9. The denominator reaches zero at that point and turns negative beyond r=38, producing a nonsensical negative 1RM. Treat any input above 35 reps as invalid; even 30-37 reps produces wildly inflated estimates.
  • Aggressive and unreliable at r=10+. Lander’s linear structure grows faster than warranted past 9.4 reps. At 15 reps, it sits 13.3 kg above Epley from the same input, enough to meaningfully overload training percentages.
  • Unvalidated by lift-specific research. Unlike Mayhew (bench-calibrated) or Epley (squat-validated by LeSuer et al.), Lander was never published with lift-specific accuracy data. Treat it as a generalist formula.
  • Sometimes confused with Lyle McDonald’s work. The formula here is Tom Lander’s, NSCA Journal 1985, with different authorship and methodology entirely. Results cited as “Lyle McDonald” have the source wrong.

How to Use the Lander Formula with the Calculator?

The one rep max calculator runs Lander alongside all six other formulas at once. Its output is most useful when the input set is 1-9 reps, where it reliably provides a conservative floor. When Lander sits noticeably above the Epley and Mayhew outputs at 10+ rep inputs, that signals your input wasn’t reliable; retest with a heavier weight for fewer reps. Use the Percentage & Rep-Max Table to convert any estimate into a full training load chart, cross-checked against the NSCA’s published training load chart.

When to use Lander versus other formulas:

  1. Use Lander when your input is 1-9 reps and you want a conservative programming floor. It consistently reads below Epley in this range, reducing the risk of overloading working sets in a new block.
  2. Use Epley for general-purpose estimation at any rep range. It’s better calibrated across both low and high rep inputs.
  3. Avoid Lander with inputs above 10 reps. At that point, Lombardi or Mayhew is the more appropriate conservative choice.

Frequently Asked Questions

The Lander formula is 1RM = (100 × w) ÷ (101.3 − 2.671 × r), where w is the weight lifted and r is the number of reps. Multiply your weight by 100, then divide by the result of subtracting 2.671 times your rep counts from 101.3. Lifting 100 kg for 5 reps gives 1RM = 10,000 ÷ (101.3 − 13.36) = 10,000 ÷ 87.94 = 113.7 kg. The linear denominator makes this one of the mathematically simplest formulas in the calculator.

At 1-9 reps, Lander is more conservative than Epley, typically 2-3 kg lower from the same input. The formulas cross at exactly 9.4 reps. Above that, Lander becomes progressively more aggressive: at 12 reps it’s 4.4 kg higher than Epley, and at 15 reps it’s 13.3 kg higher. Use Lander for a conservative estimate from a 1-9 rep input; use Epley for general-purpose estimation or when the rep count exceeds 9.

At a 1-rep input of 100 kg, Lander returns 101.4 kg, only 1.4% above the theoretical correct answer. Epley returns 103.3 kg (a 3.3% overestimate) and Mayhew returns 108.9 kg (an 8.9% overestimate). This happens because Lander’s linear denominator reduces more accurately to near-1 at r=1 than additive or exponential structures do. While 1-rep inputs are rarely used in practice, since the set is already the 1RM, Lander’s accuracy there reflects sound mathematical grounding at the formula’s anchor point.

Tom Lander published the formula in the NSCA Journal in 1985, the same year Boyd Epley published his own additive formula. Lander’s paper, “Maximum based on reps” (NSCA J. 1985;6(6):60-61), introduced the linear denominator approach. Some online sources incorrectly attribute this formula to Lyle McDonald. The calculator uses Tom Lander’s 1985 equation specifically; Lyle McDonald’s work describes different approaches with different constants and methodologies entirely.

The Lander formula becomes unreliable above roughly 10 reps and breaks completely at r≈38. The denominator (101.3 − 2.671r) reaches zero at r=37.9, producing an infinitely large estimate, and turns negative above r=38, generating nonsensical results. In practice, any input above 15 reps shouldn’t be used with this formula, and even 12-15 reps significantly overestimate 1RM compared to the other formulas in the engine.

Like all seven formulas in the calculator, Lander underestimates the deadlift 1RM, a consistent finding from LeSuer et al. (1997). Since Lander is also more conservative than Epley at low rep counts, its deadlift outputs carry a real double-underestimation risk. For deadlift estimation, add 5-10% to any formula’s output, and consider Epley or Wathan over Lander for that lift specifically.

Both Lander and Brzycki use a linear denominator structure that grows rapidly as reps increase. At r=12, Lander gives 144.4 kg and Brzycki gives 144.0 kg from a 100 kg input, indistinguishable for programming purposes. This convergence confirms that linear-denominator formulas aren’t reliable above 10-12 reps regardless of which one you’re looking at.